WASHINGTON — The more Republicans see of Mayor Giuliani, the more they seem to like him.

Recent polls show they like him even more than Senator McCain of Arizona, a development that runs counter to the way many observers thought the 2008 race would unfold.

While the former mayor introduces himself as a presidential candidate to the party rank and file in places like California, South Carolina, and Virginia, the polls suggest he is not just keeping up with Mr. McCain nationwide — he is overtaking him.

Unlike Mr. McCain or another Republican rival, Mitt Romney, Mr. Giuliani is gambling on winning over Republican voters with a message focused on national security and fiscal conservatism, to the exclusion of family values, which has been a central party tenet in recent elections.

Chiefly, he is trying to convince conservatives, at least implicitly, that social issues have to take a backseat in this election and that he is the candidate with the strongest record on key economic and security policy matters.

If Mr. Giuliani’s early campaign appearances are any indicator, that message is resonating with voters, including those who say they disagree with him on issues such as abortion.

“He is trying to convince Republicans that he is conservative. He has succeeded in convincing me,” a former member of the Republican central committee in Loudoun County, Va., Timothy Beauchemin, said after seeing Mr. Giuliani speak at a Virginia state party dinner Monday night.

Mr. Giuliani will try to further his credentials with right-wing Republicans on Friday when he addresses the Conservative Political Action Conference, a summit that will include speeches by all of the party’s 2008 hopefuls except Mr. McCain.

Mr. Giuliani heads into the forum as the leader in recent national surveys, which give him an advantage of several points over the Arizona senator. In the most surprising result, a Quinnipiac University poll released last week gave Mr. Giuliani a 22-point lead over Mr. McCain among Republicans. Most polls have Mr. Romney, the former Massachusetts governor, less than 10%, behind a one-time House speaker, Newt Gingrich, who has not entered the race.

For Mr. McCain, who ran as a party maverick against George W. Bush in 2000, the diminishing results have coincided with his refusal to back down from his support for an increase in troops in Iraq, of which he was an early and prominent advocate. Messrs. Giuliani and Romney have voiced more qualified support for President Bush’s war plan, but neither is as closely tied to the proposal as Mr. McCain.

The McCain campaign says it is not worried about his recent slump in the polls. “There will be countless polls between now and next year,” a spokesman, Danny Diaz, said. As the senator meets Republicans across the country, he said, “It’s going to become more and more clear that he’s the person that shares their perspective.”

Some Republican strategists note that although Mr. Giuliani has not launched his candidacy with a formal announcement speech, as Mr. Romney has, his heightened travel schedule and his public statements committing himself to the race have had the same effect, resulting in a bump in the polls. Mr. McCain, to some extent, has been relegated to the back burner. “His campaign hasn’t started yet,” an unaffiliated Republican consultant, Rich Galen, said.

While the presumed front-runner on the Democratic side, Senator Clinton, responded to the ascendancy of Senator Obama by jump-starting a full-fledged campaign, Mr. McCain has taken a different tack, standing back and letting Messrs. Giuliani and Romney wrestle for the spotlight. “McCain will wade in when he’s ready to wade in,” Mr. Galen said.

Mr. McCain is expected to ramp up his campaign with a formal announcement in the next month.

More than 10 months before the first primaries, Mr. McCain’s supporters are banking on the possibility that Republicans who now may be leaning toward Messrs. Giuliani or Romney will return to him once they learn more about their positions on abortion, gay rights, and gun control. Mr. Giuliani supports abortion rights, some gun control laws, and civil unions, while Mr. Romney’s positions on social issues have become markedly more conservative over the last several years.

Mr. Giuliani has sought to combat concern over his abortion stance by saying he would appoint judges who are “strict constructionists,” which many abortion opponents see as crucial to overturning the landmark Roe v. Wade decision. That statement has made some inroads among social conservatives, including the syndicated columnist Maggie Gallagher, who wrote recently that she was taking a “hard look” at Mr. Giuliani for president after never having voted for him for mayor.

But as he touts his credentials on security and tax cuts to conservative crowds, Mr. Giuliani at times seems to be waging a presidential campaign with his fingers crossed. After a speech to the conservative Hoover Institution on Monday in Washington, a questioner cited Ms. Gallagher’s column and asked Mr. Giuliani if he thought her sentiment reflected a changed political landscape in the Republican primary.
“I hope,” the former mayor responded.