Romney faced growing complaints that his campaign fumbled opportunities at the Republican convention in August on foreign unrest and, most crucially, on the U.S. economy, which is seen as Obama's weakest point. GOP activists and consultants have fretted as opinion polls suggest Obama has opened a small lead over Romney since the parties' late-summer conventions.
The unexpected video, recorded in May and released Monday, sent Romney's aides scrambling yet again.
Romney surrogate Donald Trump said: "I think he has to not apologize. ... What he said is probably what he thinks."
"The problem they have is, they are not being tough enough," Trump said in a telephone interview Tuesday on NBC's "Today" show. "I'm not saying down and dirty, but that's exactly what President Obama is doing with them. They have to get tougher or they're going to lose this campaign."
Romney refused to take back his remarks and senior adviser Bay Buchanan told CNN on Tuesday that, "as a candidate he can't worry about those he can't get."
The Obama campaign e-mailed donors asking for contributions in response.
"The man who spoke these words — who demonstrates such disgust and disdain for half of our fellow Americans — is the other side's choice for president of the United States," wrote Obama campaign manager Jim Messina. "He wants to lead our country. If we don't come through for President Obama right now, this will be the guy making big decisions that affect us and our families every single day."
In the video, Romney said 47 percent of Americans pay no income tax.
About 46 percent of Americans owed no federal income tax in 2011, although many of them paid other forms of taxes. More than 16 million elderly Americans avoid federal income taxes solely because of tax breaks that apply only to seniors, according to the nonpartisan Tax Policy Center.
In the clip released by Mother Jones, Romney also is asked about the "Palestinian problem." He gives a rambling response, then says "the Palestinians have no interest whatsoever in establishing peace" and "the pathway to peace is almost unthinkable to accomplish."
Associated Press writers Ken Thomas in Los Angeles, David Pitt in Des Moines, Iowa, and Charles Babington, Julie Pace and Philip Elliott in Washington contributed to this report.
- Britain has a new princess — and...
- Have you seen 'Age of Ultron'? Here are 50...
- Black mothers wonder if their lost babies are...
- Video: Town crier announces birth of...
- New royal baby: Destined to be a 'spare to...
- 18 of the best made-up words from children's...
- Rage to relief in Baltimore as 6 officers...
- Nigeria: Nearly 300 freed women, children led...
- Opposing sides of same-sex marriage... 124
- After historic arguments, Supreme Court... 62
- Outcome of same-sex marriage case hard... 54
- Religious liberty issues dog Supreme... 44
- Vermont Sen. Bernie Sanders: 'I am... 40
- Rage to relief in Baltimore as 6... 38
- Stewart, Bishop launch group to take... 37
- Defending the Faith: Going up to Jerusalem 23