SALT LAKE CITY (AP) — President Barack Obama declared Tuesday night the occupant of the White House must “work for everyone, not just for some,” jabbing back at Mitt Romney’s jarring statement that as a candidate, he doesn’t worry about the 47 percent of the country that pays no income taxes.

The Republican presidential challenger neither disavowed nor apologized for his remarks, which included an observation that nearly half of the country believe they are victims and entitled to a range of government support. Instead, Romney cast his comment as evidence of a fundamental difference with Obama over the economy, adding the federal government should not “take from some to give to the others.”

The sluggish economy and lingering high unemployment are by far the overriding issues of the election, and Romney’s case for the presidency is based on his claim that his success as a businessman has left him the skills needed to create jobs in a nation where unemployment is 8.1 percent.

Obama and the Democrats have tried to counter by depicting the president’s challenger as a multimillionaire who has some of his wealth invested in the Cayman Islands and elsewhere overseas, and is out of touch with the needs of middle class Americans.

As the rivals sparred with seven weeks remaining in a close race for the White House, two Republican Senate candidates — Sen. Scott Brown of Massachusetts and Linda McMahon who is running in Connecticut — publicly disavowed Romney’s remarks and Republican officials openly debated the impact that a series of controversies would have on the party’s prospects of winning the presidency.

Top Republicans in Congress declined through aides to offer their reaction to Romney’s remarks — just as they generally refrained from commenting a week ago when he issued a statement that inaccurately accused the Obama administration of giving comfort to demonstrators after they breached the U.S. Embassy in Cairo.

The most recent controversy in a campaign filled with them was ignited by the emergence of a videotape, made last May, in which Romney told donors at a fundraiser that 47 percent of Americans pay no income taxes. They “believe the government has a responsibility to care for them … believe that they are entitled to health care, to food, to housing, to you name it. That that’s an entitlement.”

He said, “I’ll never convince them they should take personal responsibility and care for their lives.”

In a next-day interview on Fox, the TV network of choice for conservatives, Romney said he didn’t intend to write off any part of a deeply divided electorate, including seniors who are among those who often pay no taxes. Instead, he repeatedly sought to reframe his remarks as a philosophical difference of opinion between himself and Obama.

“I’m not going to get” votes from Americans who believe government’s job is to redistribute wealth,” he said, adding that was something Obama believes in.

He also said he wants to be president so he can help hard-pressed Americans find work and earn enough so they become income taxpayers.

Romney didn’t say so, but the U.S. income tax is designed to be progressive, so those who earn the most theoretically pay the most. Through programs as diverse as Social Security, the government’s pension program, and Medicare, federal health insurance for the elderly, and food stamps, the government collects tax revenue and pays it out in the form of benefits for those who qualify.

Obama responded during an appearance on the late-night David Letterman television show.

“One thing I’ve learned as president is that you represent the entire country,” he said. As for Romney’s statement about the 47 percent, he said, “There are not a lot of people out there who think they are victims” or simply entitled.

At the same time, his campaign released a new ad saying that if Romney wins the White House, he might seek the elimination of a series of tax breaks used by millions of middle class Americans.

For his part, Romney referred to videotaped comments Obama made in 1998 as evidence he favored government redistribution of wealth. As an Illinois state senator at the time, Obama said he believes in it “at least to a certain level to make sure everybody’s got a shot.”

Privately, some Republicans were harshly critical of Romney’s most recent comments and his overall campaign to date, saying he had frittered away opportunities. They also noted that with early voting already under way in some states, the time to recover was smaller than might appear.

In recent days, Republicans have grumbled that Romney needed to sharpen his appeal to struggling middle class Americans by stating more clearly what he would do as president to help them. That effort began overnight with a new ad designed to appeal to female voters.

The new controversy blazed as opinion polls suggested that a narrow lead Obama gained nationally and in some key battleground states in the wake of the Democratic National Convention might be ebbing.

In his original reaction to the video, posted by the left-leaning magazine Mother Jones, Romney told reporters Monday night that his fundraising remarks were “not elegantly stated.” But he offered no apologies and did not answer directly when asked if he felt he had offended anyone.

He also called for the release of the entire video, rather than selected clips, and Mother Jones did so Tuesday afternoon.

By then, the magazine had already posted another excerpt in which Romney offered an unvarnished assessment of the chances for peace in the Middle East. “The Palestinians have no interest whatsoever in establishing peace,” and “the pathway to peace is almost unthinkable to accomplish,” he said.

“You hope for some degree of stability, but you recognize that this is going to remain an unsolved problem,” he said, “and we kick the ball down the field and hope that ultimately, somehow, something will happen and resolve it.”

On another topic, he also noted that his father was born in Mexico and suggested humorously that “I’d have a better shot at winning this” if George Romney had been born to Mexican parents. “But he was unfortunately born to Americans living in Mexico. … And I say that jokingly, but it would be helpful to be Latino.”

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Associated Press reporters Holly Ramer in Dover, New Hampshire, and David Espo, Charles Babington, Julie Pace, Philip Elliott and Kasie Hunt in Washington contributed to this report. Kuhnhenn reported from Washington.