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Washington (CNN) -- When Defense Secretary Chuck Hagel visits Dover Air Force Base Wednesday, he won't just be honoring troops killed in Afghanistan. His presence will also send a message about the government shutdown.

Hagel will attend a ceremony for the return of soldiers' remains -- at a time the families of those service members are not receiving the standard benefits typically given to them.

Due to the partial federal government shutdown, those benefits, which include a $100,000 payment, are being withheld.

It's the "worst nightmare" for military families, says Amy Neiberger-Miller of TAPS, a support network for families of the fallen.

Obama: GOP doesn't get to demand ransom

Boehner: Country is on 'dangerous path'

Newt Gingrich: Obama should negotiate

Can we tone down the shutdown rhetoric?

Lawmakers in the House are scheduled to vote Wednesday to resume "appropriations for death gratuities and related survivor benefits."

Also Wednesday, the House Democratic caucus is invited to a meeting at the White House in the afternoon to discuss the shutdown and the need for a debt limit increase, a White House official told CNN. Other caucuses will be invited in the coming days, the official said.

The plight of military families is just the latest fallout from the shutdown as it enters Day 9.

President Barack Obama said Tuesday he is ready to talk, even on Republicans' terms, as long as Congress acts first to end the shutdown and raise the debt ceiling -- even for a short period.

At a news conference, Obama indicated Republicans could essentially set the agenda for budget negotiations, but only if Congress agrees first to a short-term spending plan to fund the government and to raise the federal borrowing limit to avoid a possible first-ever U.S. default next week.

"I will talk about anything," the president said.

House Speaker John Boehner, speaking Tuesday afternoon after what he called a "pleasant" but ineffectual phone call with Obama, promptly rejected the president's comments as nothing new.

"What the president said today was if there's unconditional surrender by Republicans, he'll sit down and talk to us," Boehner said. "That's not the way our government works."

At the same time, Boehner said he's "hopeful" top Republicans and Democrats could soon begin a "conversation."

"There's going to be a negotiation here," the Ohio Republican said. "We can't raise the debt ceiling without doing something about what's driving it to borrow more money and live beyond our means."

Yet while Boehner didn't indicate any points of agreement, a senior House Republican told CNN that GOP members may be willing to go for a short-term debt ceiling hike -- lasting four to six weeks -- as long as the president agrees negotiations will occur during that time.

Still, it's no guarantee such a measure would be supported by a majority of Republicans, something that Boehner has traditionally required before calling any vote in the House.

A second GOP source says the White House drawing a line in the sand not to negotiate has further complicated matters. Republican leaders have talked, though, to CEOs who called them at the request of Treasury Secretary Jack Lew and senior presidential adviser Valerie Jarrett.

And if there's no breakthrough? The shutdown -- which began October 1, after the GOP-led House tied its funding measures to dismantling or defunding Obama's signature health care reform law -- continues. Plus, another crisis looms October 17, when the Treasury Department says the U.S. government must raise the amount of money it can borrow or else be unable to pay its bills.

All the partisan bickering -- and lack of progress -- is taking its toll not just on furloughed workers, shuttered government facilities and programs, but also on Americans' confidence in their government.

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The game is the same, but many of the players have changed. Congress and the president are facing off in another supreme spending showdown. If they don't agree on a funding bill by the end of September 30, much of government will shutdown. This last happened in 2011, when Congress avoided a shutdown by passing a spending measure shortly after the midnight deadline hit. Who controls what happens this time? Take a look at the key players who will determine how this fight ends: -- From CNN Capitol Hill Reporter Lisa Desjardins. CNN's Deirdre Walsh and Ted Barrett contributed to this report.

Rep. Mark Meadows, R-North Carolina -- The architect. During Congress' August recess, the tea party-backed freshman wrote to Republican leaders suggesting that they tie dismantling Obamacare to the funding bill. Though initially rejected by GOP leadership, 79 of Meadows' House colleagues signed on to the letter, which quoted James Madison writing in the Federalist Papers, "the power over the purse may, in fact, be regarded as the most complete and effectual weapon ... for obtaining a redress of every grievance."

Speaker John Boehner, R-Ohio -- The coach. He'll make the key play call. The top Republican leader in the land may be the most important player in the days immediately before a possible shutdown. Boehner could decide whether to push through the Senate's version of a spending bill and keep government running, or he could float a third version with some other Republican wish list items in it. If he takes the second option, Boehner could risk a shutdown but could also force the Senate into a tough position: give House Republicans something or send federal workers home. Timing on all this will be critical.

Sen. Ted Cruz, R-Texas -- The revolutionary or rabble rouser, depending on your viewpoint. The tea party firebrand could lead a long filibuster on the Senate floor, delaying passage of a spending bill until just one day before the deadline on Monday, September 30. Cruz has stoked the anti-Obamacare flames all summer, but recently angered fellow Republicans by openly saying that the Senate does not have the votes to repeal the health care law.

Sen. Marco Rubio, R-Florida -- Senator to watch. The potential presidential candidate has been one of three senators (Cruz and Mike Lee, R-Utah, being the others) pushing to use the government shutdown debate as a way to repeal or defund Obamacare. But watch his actions and language as a shutdown nears to see if he digs in or if downshifts at all.

Sen. Harry Reid, D-Nevada -- The man steering the ship in the Senate. Master at using Senate procedure to his advantage, Reid is the main force in controlling the voting process in the chamber and ensuring that an attempted filibuster by tea party-types fails. The majority leader will be a primary negotiator if we reach phase three, if the House does not accept the Senate spending bill.

Sen. Mitch McConnell, R-Kentucky -- If Reid steers the ship, McConnell controls the headwinds. Which is good news for Reid, at least initially. The Republican leader and several of his members say they will vote against Cruz's filibuster and in favor of a spending bill with no limits on Obamacare. Meaning, in favor of a bill that just funds government. McConnell generally has been leery of running into a shutdown or default. In fact, one legislative method for avoiding default is named after him.

Sen. Patty Murray, D-Washington -- The consigliore. Murray, center, does not seek the outside limelight, but the Senate Budget Committee chairwoman is a major fiscal force behind the scenes on Capitol Hill. Known by fellow Democrats as a straight shooter, she is also an experienced negotiator, having co-chaired the laborious, somewhat torturous and unsuccessful Super Committee.

Rep. Tom Graves, R-Georgia -- The new militia leader. The freshman congressman from Georgia, second from right, is one reason the debate has reached this point. Graves led the charge that blocked the original proposal by House Republican leaders. That would have kept government funded and had a detachable portion on Obamacare. Instead Graves and other conservatives forced their leaders to pass a spending bill with a mandatory defunding of Obamacare.

Rep. Peter King, R-New York -- The blunt statesman. King is outspoken against many tea party tactics, calling the move to tie Obamacare to the must-pass spending bill essentially a suicide mission and Cruz "a fraud." He is pushing for Republicans to accept a more "clean" spending bill that can pass the Senate and avoid a shutdown.

Thomas Donohue, president and CEO of the U.S. Chamber of Commerce -- The heavy. Donohue is known for his deep connections and his aggressive lobbying on behalf of business. He and the Chamber are urging Republican lawmakers to avoid a shutdown. The Chamber is an important political backer for conservatives, but has had mixed success with the current Congress, locking in firm anti-tax positions but unable to push through immigration reform so far.

Michael Needham, president of Heritage Action -- The driving force. Needham runs the political offshoot of the conservative Heritage Foundation and has been unrelenting in urging lawmakers to repeal Obamacare. He has told Republicans not to fear a potential shutdown, saying they would suffer more politically from allowing Obamacare to continue.

President Barack Obama -- The campaigner and CEO. Expect the president to use his podium more as a shutdown nears, aiming at public opinion as Democrats in Congress position themselves. If House Republicans send back a new proposal close to the September 30 deadline, the president and Democrats will have to decide what move to make next.

Rep. Eric Cantor, R-Virginia -- The powerful lieutenant. Cantor, the House Republican No. 2, is much more closely allied with conservatives and tea party members in the House than is Speaker Boehner. The two have not always agreed on every strategy during potential shutdown debates, but have been in public lockstep during the current go-around.

Rep. Nancy Pelosi, D-California, and Steny Hoyer, D-Maryland -- Players on deck. The top two House Democrats are mostly watching and waiting. But they will play a critical role once Boehner decides his next move. They could either bring Democratic votes on board a deal or be the loudest voices against a new Republican alternative. Hoyer will be interesting to watch; he has strongly opposed both the House and Senate plans as cutting too much in spending.

Rep. Kevin McCarthy, R-California -- The numbers guy. McCarthy, the House whip, has the tricky job of assessing exactly where Republican members stand and getting the 217 votes it takes to pass a bill in the chamber. He is known for his outreach to and connection with many of the freshmen House members who align with the tea party.

Rep. Paul Ryan, R-Wisconsin -- Member to watch. The vote of the House budget chairman and former vice presidential nominee is an important signal both within Republican ranks and to the public at large. Ryan has voted against some funding measures in the past, including the emergency aid for Superstorm Sandy recovery. But he was a "yes" on the last extension of the debt ceiling.

Rep. Ileana Ros-Lehtinen, R-Florida -- Another member to watch. A former committee chairwoman (Republican rules have term limits for committee chairs), Ros-Lehtinen knows House politics and procedure inside out. Depending on the issue, she has been described as a conservative or moderate, and occasionally as a libertarian.

Key players in the shutdown debate

Key players in the shutdown debate

Key players in the shutdown debate

Key players in the shutdown debate

Key players in the shutdown debate

Key players in the shutdown debate

Key players in the shutdown debate

Key players in the shutdown debate

Key players in the shutdown debate

Key players in the shutdown debate

Key players in the shutdown debate

Key players in the shutdown debate

Key players in the shutdown debate

Key players in the shutdown debate

Key players in the shutdown debate

Key players in the shutdown debate

Key players in the shutdown debate

Key players in the shutdown debate

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Photos: Key players in the shutdown debate

Looking directly in the camera, Obama acknowledged frustrations with what's going in Washington in terms of the current impasse and all the other budgetary battles preceding it.

"We've got to stop repeating this pattern," the president said. "I apologize you have to go through this stuff every three months, it seems like. And Lord knows, I'm tired of it. But at some point we've got to break these habits."

Poll: Most angry at both parties

While the two parties blame each other in Washington, outside the capital few get off easy.

Shutdown forecast: Week two and clouds ahead

In a national poll released Monday, most respondents said the government shutdown was causing a crisis or major problems for the country.

The CNN/ORC International survey indicated that slightly more people were angry at Republicans than Democrats or Obama for the shutdown, though both sides took a hit.

According to the poll conducted over the weekend, 63% of respondents said they were angry at the Republicans for the way they have handled the shutdown, while 57% expressed anger at Democrats and 53% at Obama.

"It looks like there is more than enough blame to go around, and both parties are being hurt by the shutdown," said CNN Polling Director Keating Holland.

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CNN's Jim Acosta, Deirdre Walsh, Barbara Starr, Ted Barrett, Greg Botelho, Dana Bash and Brianna Keilar contributed to this report.