The debate was Wednesday night at the University of New Hampshire in Durham without Thompson, who later made his formal declaration on "The Tonight Show with Jay Leno."

The New York Times said the toughest bickering was over illegal immigration, with former Massachusetts Gov. Mitt Romney accusing Rudy Giuliani of attracting illegal immigrants when he was the mayor of New York.

Giuliani replied he was dealing with a federal government that wasn't deporting illegal immigrants.

Sen. John McCain of Arizona took on Romney for saying the new strategy in Iraq was "apparently" working.

"It is working," McCain said. "No, not 'apparently.' It's working."

The debate, the fifth in the run-up to the 2008 election was also attended by Sen. Sam Brownback of Kansas, former Arkansas Governor Mike Huckabee, Rep. Tom Tancredo of Colorado, Rep. Duncan Hunter of California and Rep. Ron Paul of Texas.