The government "is spending money of future generations and those yet to be born," added, making his debate debut after a late entry into the race. He said future retirees should receive smaller Social Security benefits than they have been promised.
Thompson played it safe while Giuliani and Romney argued over taxes, reports CBS News correspondent Nancy Cordes.
"With all eyes on Thompson, he performed about as he has throughout the campaign thus far - marginally well but not particularly jumping off the charts," wrote CBSNews.com senior political editor Vaughn Ververs in Horserace.
After months of polite debate sparring, Giuliani and Romney squared off without hesitation, a reflection of their struggle for primacy in the race for their party's presidential nomination.
"I cut taxes 23 times. I believe in tax cuts," said Giuliani, former mayor of New York and leader in national Republican polls.
Romney in turn criticized his rival for once filing a court challenge to a law that gave President Clinton the right to veto spending items line by line. "I'm in favor of the line item veto," he said, adding he exercised it 844 times while governor of Massachusetts.
Romney also said that while mayor, Giuliani "fought to keep the commuter tax, which is a very substantial tax ... on consumers coming into New York."
The former governor leads his rivals in the polls in Iowa, where caucuses will be the first contest of the campaign, and he and Giuliani are in a close race in surveys in New Hampshire, the leadoff primary state.
Giuliani responded that spending fell in New York while he was mayor, and rose in Massachusetts while Romney was governor.
"The point is that you've got to control taxes. I did it, he didn't. ... I led, he lagged."
"It's all baloney," retorted Romney. "I did not increase taxes in Massachusetts. I lowered taxes."
The clash was among the most heated of the campaign for the Republican presidential nomination, reflecting a quickening pace as the 2008 caucuses and primaries draw close.
It also left Thompson and the other contenders as something of bystanders for the several moments that Romney and Giuliani went at one another.
All nine of the men on stage sought to stress their conservative economic credentials throughout the two-hour debate, held in the city that gave birth to the Ford Motor Co. more than a century ago.
Sen.of Arizona said President Bush was right to veto a children's health expansion bill, and he urged him to reject a multibillion-dollar public works measure as well.
"We've got to get wasteful spending under control," he said.