Santorum, surging in the race, also took his lumps from the audience, which booed when he said he had voted several years ago for the No Child Left Behind education legislation even though he had opposed it.
"Look, politics is a team sport, folks," he said of the measure backed by Republican President George W. Bush and other GOP lawmakers.
With pivotal primaries in Arizona and Michigan just six days distant - and 10 more contests one week later - Romney and Santorum sparred more aggressively than in past debates, sometimes talking over each other's answers.
Texas Rep. Ron Paul chimed in from the side, saying with a smile that Santorum was a fake conservative who had voted for programs that he now says he wants to repeal. Former House Speaker Newt Gingrich acted almost as a referee at times.
On foreign affairs, all four Republicans attacked President Barack Obama for his handling of Iran and its attempt to develop a nuclear program, but none of the contenders advocated providing arms to the rebels trying to topple the government of Syrian President Bashar Assad.
The most animated clash of the evening focused on health care in the United States.
Santorum said that Romney had used government money to "fund a federal takeover of health care in Massachusetts," a reference to the state law that was enacted during Romney's term as governor. The law includes a requirement for individuals to purchase coverage that is similar to the one in Obama's landmark federal law that Romney and other Republicans have vowed to repeal.
In rebuttal, Romney said Santorum, a former Pennsylvania senator, actually bore responsibility for passage of the health care law that Obama won from a Democratic-controlled Congress in 2010, even though he wasn't in office at the time. Romney said that in a primary battle in 2004, Santorum had supported then-Sen. Arlen Specter of Pennsylvania, who later switched parties and voted for the law Obama wanted.
"He voted for Obamacare. If you had not supported him, if we had said no to Arlen Specter, we would not have Obamacare," Romney contended.
Santorum was the aggressor on bailouts.
While all four of the Republicans on the debate stage opposed the federal bailout of the auto industry in 2008 and 2009, Santorum said he had voted against other government-funded rescue efforts.
"With respect to Governor Romney that was not the case, he supported the folks on Wall Street and bailed out Wall Street - was all for it - and when it came to the auto workers and the folks in Detroit, he said no. That to me is not a principled consistent position," he said.
The debate had a different look from the 19 that preceded it. Instead of standing behind lecterns, the four presidential rivals sat in chairs lined up side by side. Romney, Santorum and Paul recently announced they would not participate in another four-way appearance that had been scheduled in Atlanta, raising the possibility that the 20th debate might be the last.
There was another difference, as well, in the form of polls that underscored the gains that Obama has made in his bid for re-election.
An Associated Press-Gfk poll released Wednesday found that Obama would defeat any of the four remaining Republican contenders in a hypothetical matchup. It also found that the nation is showing more optimism about the state of the economy, the dominant issue in the race.
But for two hours, Romney, Santorum, Paul and Gingrich had a different campaign in mind, their own race for the Republican nomination and the right to oppose Obama in the fall.
After a brief lull, the campaign calendar calls for 13 primaries and caucuses between next Tuesday, when Arizona and Michigan have primaries, and March 6, a 10-state Super Tuesday. The Washington state caucuses are March 3.
Romney is campaigning confidently in Arizona, so much so that his campaign has not aired any television ads.
But the former Massachusetts governor faces an unexpectedly strong challenge in his home state of Michigan, where Santorum is hoping to spring an upset. Santorum's candidacy has rebounded in the two weeks since he won caucuses in Minnesota, Colorado and a non-binding primary in Missouri.
The result is a multimillion-dollar barrage of television commercials in Michigan in which the candidates and their allies swap accusations in hopes of tipping the race.
In all, 518 Republican National Convention delegates are at stake between Feb. 28 and March 6, three times the number awarded in the states that have voted since the beginning of the year. It takes 1,144 to win the nomination.
The dynamic of the campaign - Santorum challenging Romney - made their clashes Wednesday night inevitable.
Romney said Santorum voted five times while in Congress to raise the government's ability to borrow, supported retention of a law that favors construction unions and supported increased spending for Planned Parenthood. He said federal spending had risen 78 percent overall while the former Pennsylvania senator was in Congress.
Santorum retorted that government spending declined as a percentage of the economy when he was in the Senate, and he noted that when Romney was asked last year if he would support a then-pending debt-limit increase, "he said yes."
There was a clash over federal spending earmarks, as well, and Gingrich sought to intervene as if serving as a referee instead of a debate participant.
He said he supported the earmarks that Romney had sought for the Olympics in Salt Lake City in 2002, but then he accused Romney of observing a double standard by running television ads attacking Santorum for having voted for different earmarks.
He said it was silly for Romney to take the position that "what you got was right and what he got was wrong."
In the hours leading to Wednesday night's debate, Romney called for a 20 percent across-the-board cut in personal income taxes as part of a program he said would revitalize the economy and help create jobs. The top tax rate would drop from 35 percent to 28 percent, and some popular breaks would be scaled back for upper-income taxpayers. However, aides provided scant details.
"We've got to have more jobs, less debt and smaller government, they go together," Romney said in an appearance in nearby Chandler. "By lowering those marginal rates, we help businesses that pay at the individual tax rate to have more money so they can hire more people."
Romney's proposal sharpened his differences with Obama, who favors allowing tax cuts enacted under President Bush to expire on higher incomes.
Santorum, who has emerged as Romney's leading challenger in the Republican race, campaigned at a tea party gathering in Tucson, where he said his rival's new tax proposal largely mirrored one he had had already made.
"Welcome to the party, governor, it's great to have you along," he said.
Santorum's rise in the race has left Gingrich and Paul on the outside looking for a way in.
The former House speaker has yet to recover from a campaign nosedive that began after he won the South Carolina primary on Jan. 21, and he is pinning his hopes on his home state of Georgia to begin a comeback on March 6.
His campaign announced plans Wednesday to buy 30-minute blocks of television time in upcoming primary and caucus states for an infomercial on reducing energy prices.
Gingrich's decision not to campaign in Michigan so far has allowed Santorum to compete against Romney without also having to fend off a rival for the votes of conservatives.
Paul has yet to win any primaries or caucuses.
He has weighed in against Santorum, though, airing an ad in Michigan that challenges the former senator's claim of taking a conservative line against federal spending. The ad says Santorum voted to raise the debt limit five times, and also supported legislation that created a prescription drug benefit under Medicare.
Associated Press writers Kasie Hunt and Charles Babington contributed to this story