Obama himself headed for New York for an appearance on David Letterman's TV couch and a fundraiser with Beyonce and Jay-Z.
Romney planned no apology but was expected to respond to questions about the video by reinforcing the reaction he delivered Monday night: that Obama favors "a government-centered society" with people dependent on public support.
Obama's campaign, seeing an opportunity to build on its earlier efforts to cast the Republican as out of touch with average Americans, emailed a fundraising appeal to supporters and posted a video online asking voters to watch Romney's comments and respond.
"I actually felt sick to my stomach," one woman says in the web video.
Another woman says, "That's not somebody who I'm thinking, 'Oh, I want him as my president.'"
Romney advisers concede the video came at a bad time - seven weeks before Election Day and with early voting beginning in two dozen states by this weekend. They acknowledge the remarks may dominate news coverage for days but dispute the notion that Romney's comments could fundamentally change the election.
The unscripted moment was reminiscent of the 2008 campaign, when Obama was caught telling the wealthy wing of his party at a private fundraiser in San Francisco that some residents of depressed rural areas get bitter and "cling to guns or religion or antipathy to people who aren't like them."
In the Romney video, recorded at a Florida fundraiser in May, the candidate says 47 percent of Americans don't pay taxes and believe they are entitled to extensive government support.
"My job is not to worry about those people," he said.
After the video posted late Monday afternoon on Mother Jones magazine's website, Romney told reporters that while his comments were "not elegantly stated," he stood by his remarks.
"Those who are reliant on government are not as attracted to my message of slimming down the size of government," Romney said in Costa Mesa, Calif., doubling down on his statement.
Romney running mate Paul Ryan focused on the limited-government argument while campaigning in New Hampshire, without mentioning the video. He mistakenly called it the "Ryan-Romney plan" for a stronger middle class before correcting himself and promising the two would put Americans back to work rather than encourage dependency on government.
Vice President Joe Biden, campaigning in Iowa, declined to comment on the video. "I'll let his words speak for themselves," Biden said while shaking hands with voters after a speech in Ottumwa.
A pro-Obama super political action committee quickly pushed up the air date for a new television advertisement in response to the video.
The ad, from Priorities USA Action, was previously shown online and never mentions the Romney video because it was produced before it became public. But the super PAC says it believes the ad's message serves as a counter to the Republican nominee's words and bought time to begin airing it as early as Tuesday on stations in Colorado, Florida, Iowa, Ohio, Virginia and Wisconsin.
"Doesn't Mitt Romney understand we can't rebuild America by tearing down the middle class?" the narrator says. The group also is likely to start running new ads using Romney's words from the fundraising video.
Obama was told about the video Monday afternoon by staff traveling with him on a campaign trip to Ohio. White House Press Secretary Jay Carney declined to say whether Obama had watched the video or to characterize the president's reaction to Romney's remarks.
"Setting aside what Gov. Romney thinks, I can tell you that the president certainly doesn't think that men and women on Social Security are irresponsible or victims, that students are irresponsible or are victims," Carney said.
The president has not publicly commented on the video, but could do so Tuesday when he tapes an interview with David Letterman and delivers remarks at a fundraiser at the Waldorf Astoria hotel. After that, Obama was set to collect nearly $4 million at a $40,000-a-ticket fundraiser at a Manhattan nightclub with husband and wife musicians Jay-Z and Beyonce.
Romney had no public appearances scheduled Tuesday and planned to raise money in Salt Lake City and in Dallas with former first lady Laura Bush at the Bushes' Texas home.
Looking to change the subject, Romney's campaign rolled out a new television ad featuring a mother and infant, aimed at cutting into Obama's advantage with female voters. It argued that Obama's economic policies would make women's lives harder.
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."
Colorado Senator Mark Udall responded to Romney's statement, saying: "You really know the character of an individual by what they say in private. And, yes, this is an election about the economy and jobs. But, it's also an election about character and vision."
(Copyright 2012 by The Associated Press. All Rights Reserved.)