GIUILIANI:

Illegal immigration has become a key issue in the Republican presidential caucuses and primaries that begin in Iowa on January 3.

The Republican contenders also debated Iraq.

Former Senator Fred Thompson of Tennessee was asked by a YouTube questioner how long U.S. troops should remain in Iraq.

"We should not be there any longer than necessary, and we do not know how long that will be, but we should be there absolutely as long as it takes to complete our mission there," he said.

Texas Congressman Ron Paul remains the only Republican presidential contender who supports an immediate withdrawal from Iraq.

"The best commitment we can make to the Iraqi people is to give them their country back," he said.  "That is the most important thing we can do."

Paul's answer drew a response from Senator John McCain of Arizona, who noted an improved security situation in Iraq as a result of the U.S. troop surge.

"I just finished having Thanksgiving with the troops, and their message to you is, 'Let us win, let us win,'" said Senator McCain.

Previous Republican debates featured attacks from several of the candidates on Senator Hillary Clinton, the frontrunner for the Democratic Party's presidential nomination.

There were fewer jabs at Clinton in this debate, though former Arkansas Governor Mike Huckabee did manage to work in her name in an answer to a question about future space exploration.

"Whether we need to send somebody to Mars, I do not know.  But I will you tell what.  If we do, I have got a few suggestions, and maybe Hillary [Clinton] could be on the first rocket to Mars," he said.

Huckabee appears to be on the move in the latest poll in the early contest state of Iowa.  A new survey by the Rasmussen Reports shows Huckabee vaulting into a narrow lead in Iowa over Romney, who retains the lead in the early voting state of New Hampshire, while Giuliani continues to lead the Republican field in national polls.