Campaigning in South Carolina last week, he said that Democrats too often win over black voters by telling them "we'll take care of you with free stuff". Romney made similar comments during his 2012 bid and Democrats said that Bush's remarks were part of a pattern of Republicans insulting minority voters.
His comments could undercut what Bush allies argue would be his great strength in a general election contest: A cultural fluency that would give him crossover appeal to a diverse electorate.
Party strategists said that Bush must find a way to recharge his campaign with a compelling message about his conservative governing record as Governor of Florida.
"People assume that they know who Jeb Bush is, and that's part of the struggle the Bush campaign has," said Republican strategist Henry Barbour.
"I think if people get to know Jeb and they give him a chance, he's going to be tough to beat," Barbour added. "But they don't know him yet. And you've got a right wing of the party that is almost determined not to get to know him. They want to believe that because they disagree with him on a couple issues that he's not their guy."
Appearing on Fox News, Bush played down the importance of his standing in current polls. "These polls really don't matter," he said. "They don't filter out the people that aren't going to vote, it's just - I know it's an obsession because it kind of frames the debate for people for that week."
As the son and brother of former presidents, Bush is a member of the Republican's establishment wing, which has suffered setbacks in recent days. House Speaker John Boehner - who publicly encouraged Bush to enter the race - announced plans to resign after dozens of conservative legislators threatened to oust him. And Walker's sudden departure from the presidential race came as support shifted to outsider candidates.
Given those developments, Bush "needs to get his favourables up," said a senior Republican bundler who is backing him.
"People are looking at the stage and saying: 'Jeb and Marco? I'm going with the new,' " said a top party fundraiser not aligned with a campaign. "You're seeing people really gravitate to him and saying, 'Okay, we'll buck the Bush machine.'"
"What I hear everywhere when you say Jeb's name is, 'If you want to lose the general election, nominate Jeb," the fundraiser added.
But those within the Bush camp say they are not yet alarmed over the dynamics of the race, confident that their financial war chest will enable him to outlast opponents, according to campaign strategists and top Republicans familiar with internal discussions. In private conversations, however, Bush advisers betray signs of anxiety about Rubio's rise.
"They are prepared for a long, grinding fight and being the last person standing," the Republican fundraiser said. "But they are concerned about the trends and they are concerned about Marco."
Rubio has jumped ahead of Bush in recent polls of Republicans in New Hampshire and Florida - two states critical to Bush's campaign strategy. In New Hampshire, a CNN/WMUR poll released last week gave Donald Trump a commanding 26 per cent lead. Rubio was third with 9 per cent and Bush tied with Ohio Governor John Kasich for fifth place, with 7 per cent. A Florida Atlantic University poll released last week gave Trump 31.5 per cent among Sunshine State voters. Rubio 19.2 per cent and Bush 11.3 per cent.
Bush maintains a huge financial advantage over Rubio - he had roughly US$120 million between his campaign and an allied super PAC at the end of June.
