Appearing with former U.S. House Speaker Newt Gingrich of Georgia and U.S. Rep. Ron Paul of Texas in a debate televised by CNN, Santorum came under fire from Romney for having voted for so-called earmarks while in Congress.
Romney, a former governor of Massachusetts, said federal government spending grew by 80 percent during Santorum's time in the U.S. Senate. He said he would ban congressional earmarks.
"The earmark process is broken," he said, describing a process in which Congress appropriates funds, often for projects and programs in members' home districts.
"You're misrepresenting the facts," Santorum, who is from Pennsylvania, told Romney. "You don't know what you're talking about."
He said Congress "has a role of allocating resources when they think the administration is wrong."
During a discussion about the government's role in health issues, including contraception, Gingrich accused President Barack Obama of voting to protect doctors "who commit infanticide" when he was an Illinois state senator and Romney said Obama has attacked religious liberty more than any other president.
On the issue of the debt and deficit, Gingrich said he would work to repeal U.S. civil service laws and replace them with "a modern management system."
Paul criticized Santorum for saying he would work to repeal the No Child Left Behind law, which he had voted for while in the Senate.
"It loses credibility is what our problem is," Paul said. "The American people are sick and tired of Congress. They get about a 9 percent rating."
Romney and Santorum are in a statistical dead heat in primary state Arizona, a poll indicated ahead of the debate, the 20th of the primary season and the first since the candidates met in Jacksonville, Fla., Jan. 26.
The debate was to be the last before the Arizona and Michigan primaries Feb. 28 and the 10-state Super Tuesday primaries March 6. Super Tuesday involves contests in Alaska, Georgia, Idaho, Massachusetts, North Dakota, Ohio, Oklahoma, Tennessee, Vermont and Virginia.
Thirty-six percent of likely Republican voters back Romney, while 32 percent support Santorum, a CNN/Time/ORC International poll released Tuesday indicated.
The Friday-Monday telephone poll of 467 registered Republicans likely to vote in Tuesday's Arizona primary, has a margin of error of 4.5 percentage points. With the 4-percentage-point separation, the two candidates are in a statistical dead heat.
Gingrich ranks third in the poll, with 18 percent support, followed by Paul with 6 percent. Six percent are unsure and 2 percent preferred someone else or wanted none of the candidates, the poll indicated.
Romney, who grew up in Michigan, is scrambling to stop Santorum from defeating him in his home state.
Romney -- whose late father, George Romney, led former automaker American Motors Corp. from 1954 to 1962 before becoming Michigan governor from 1963 to 1969 -- has taken some criticism in Michigan for arguing against the auto industry's government bailouts, saying a managed bankruptcy would have been a better option.
Romney made a comment about taxes and spending Tuesday that his campaign felt a need to clarify.
"If you just cut -- if all you're thinking about doing is cutting spending -- as you cut spending, you'll slow down the economy," Romney said Shelby Township, Mich., 25 miles north of Detroit, at a town hall-style meeting.
"So you have to, at the same time, create pro-growth tax policies," Romney said.
His comment was pounced on by conservatives.
"It confirms yet again that Romney is not a limited-government conservative," Andy Roth, vice president for government affairs at the fiscally conservative Club for Growth, told MSNBC.
Romney spokesman Ryan Williams later said, "The governor's point was that simply slashing the budget, with no affirmative pro-growth policies, is insufficient to get the economy turned around."
But Romney "believes that budget cuts -- especially in the context of President [Barack] Obama's unprecedented spending explosion -- are a step in the right direction," Williams said.
Romney plans to announce an economic plan in Detroit Friday that he said Tuesday would integrate his views on tax policy, spending and entitlement reform into a single package.