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Washington (CNN) -- Jeb Bush was blitzed with questions Thursday about his presidential ambitions in a private session with top South Carolina donors and business leaders, multiple sources at the meeting told CNN.

Bush was politely non-committal, as he is in public, but said he was seriously considering the possibility and would make a decision after the holiday season.

Bush, brother to one former president and son of another, was also pressed on whether he thought his last name would be a liability in a national campaign.

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The former Florida governor responded that "he quit worrying about that a long time ago," according to two people in the room.

"He said that everybody has things about them that are positives and negatives, but he said he loves his brother and loves his father, and that every campaign is about telling people who you are," said one source. "He said that my last name is the same, but I am not them. That my job is to show people who I am as a policy maker and a man, and that's the same job everyone else has."

The former Florida governor was in the state, which happens to hold the first presidential primary in the south, for a round of campaigning with South Carolina Gov. Nikki Haley, who is expected to win re-election next month.

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Bush has traveled the country raising money for Republican candidates this cycle, but the South Carolina visit marked his first trek to an early primary state as questions about his national ambitions build.

Following crowded public events in Greenville and Lexington, Bush headlined a fundraiser for Haley in Columbia that included a high-dollar roundtable with about 30 of the state's leading lobbyists, business leaders, and Republican officials including Pamela Lackey, the president of AT&T South Carolina, Mikee Johnson, head of the South Carolina Manufacturers Alliance, and former state Attorney General Henry McMaster.

In the roundtable — where price of entry was $10,000 — Republicans exchanged pleasantries with Bush about his family before diving into questions about his political future.

"This wasn't a politically agnostic business crowd," said one person in the room who did not want to be identified. "They dialed right in and wanted to get into politics, the horse race of 2016."

Bush, this person said, was "very engaging, but he was very non-committal about running. He said he has to have joy in his heart to do it. And he said he gets the question wherever he goes."

Ed McMullen, a Republican lobbyist in Columbia, said the response to Bush from the donor crowd was "unbelievable."

"He said that if I am going to run, I would run because I have a positive vision to take the country forward and unify people and do something that the other people in the race are not talking about," McMullen said. "He had that positive Reagan vision of creating a majority that transcends parties and races and brings people together. I'll tell you what, he makes it very easy to be for him."

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At one point, Bush expressed annoyance with the polarizing fights and constant negativity of the political news media — he singled out Fox News, saying he usually watches the channel for a few minutes a day before switching over to SportsCenter — and said he is "frustrated" by the toxic climate in Washington. Republicans, though, need to do more than just criticize President Barack Obama, he added.

"He said, 'It's easy to criticize. I turn on the news. I am frustrated. I get the temptation. But that can't be the only reason that people elect you, that you're not the other guy," one source at the fundraiser recalled. "The next Republican has to run about their ideas and what they will do. I get the temptation but that can't be the only reason that people elect you is that you're not the other guy."

Bush told the donors he admires the restraint of his brother, former president George W. Bush, for not criticizing Obama even as the security situation in Iraq deteriorates.

"He talked about how proud he was of his brother," said one GOP donor. "He said, I couldn't do it, but what a class act that he knows it's not his place to come out and publicly criticize the sitting president. He said it's tearing his brother up."

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