Yet a close look suggests his support from the GOP's potent right wing is less than meets the eye, according to recent Associated Press-Ipsos polls.
Conservatives, evangelical and born-again voters, and strongly loyal Republicans who back Giuliani tend to be less conservative, less religiously active and less supportive of President Bush than those favoring, Giuliani's chief rival so far, the surveys show.
That leaves Giuliani, the Republican front-runner, with a tenuous hold on the most intensely conservative voters long considered his party's core.
Giuliani and Thompson are each backed by about one-fifth of conservatives, with an equal share undecided and the rest spread among other candidates. Thompson has a slight edge over Giuliani - with undecideds close by - among right-leaning voters like Southerners, strongly loyal Republicans and people who attend religious services at least weekly.
With state primaries and caucuses less than three months away, this lack of conservative consensus creates an opportunity for Thompson and others to Giuliani's right.
"I'm concerned about his ability to hold to some conservative things I value" like opposing abortion, Sheryl Tolson, 45, a teacher and conservative from Elk Grove, Calif., said of Giuliani. Her choice is former Massachusetts Gov..
Ardent conservatives can be difference-makers in elections because of their numbers and activism, especially in Republican primaries.
While Giuliani's strongest appeal is to centrists, the former New York mayor hopes to maximize conservative support. He and other GOP presidential contenders will address a convention of Christian conservatives in Washington this weekend.
Danny Hyde, 48, a conservative from Canton, Ga., typifies the right's fragmentation.
The real estate broker said he likes Thompson and former Arkansas Gov.because they have "the pulse of the common man" and for their conservative views. Yet he may back Giuliani, whom he thinks has the best shot of defeating Sen. , D-N.Y., who sits atop the Democratic field.
"It's still a tough call," said Hyde.
While combined data from AP-Ipsos polls this month and last show Giuliani holding his own among conservatives, they also show a slender Thompson advantage among the strongest conservatives.
Of those calling themselves very conservative, the former Tennessee senator and actor leads Giuliani by 26 percent to 15 percent. Thirty-seven percent of Thompson's support comes from the very conservative, about double Giuliani's rate.
Just 37 percent of Giuliani's conservatives call themselves strongly Republican, compared to 52 percent of Thompson's.
While 22 percent of Giuliani's evangelical or born-again Christian supporters say they are very conservative, 47 percent of Thompson's do.
Sixty-four percent of Giuliani's supporters approve of Bush's performance, compared to 78 percent of Thompson's.
Thirty-seven percent backing Giuliani attend religious services at least weekly, making him the only major GOP hopeful who gets less than half his support from people who go that often.
Interviews with Republicans surveyed and conservative leaders show part of Giuliani's allure is the tough anti-terror reputation he developed after the Sept. 11 terrorist attacks on his city while he was mayor.
"If it wasn't a time of war, I wouldn't vote for him" because of his social views, said Alex Dragonchuck, 24, a conservative and truck driver from Pasco, Wash. He added, "You get a couple of nukes going off on American soil, and what good is the other stuff? You've got to prioritize."
Yet many wrestle over backing a candidate who embodies their values or one they think can win the White House.
"I can't vote for a pro-choice candidate," Richard Land, who heads the Southern Baptist Convention's public policy arm, said of Giuliani. But he added, "I'm not going to criticize anybody who says, 'I think Rudy Giuliani is the lesser of two evils"' compared to Clinton.
Rep. Pete Sessions, R-Texas, a conservative working with Giuliani's campaign, said the candidate is faring well with conservatives and cannot win the nomination without them. He said as mayor, Giuliani took actions "which Christians strongly identify with," like removing pornography shops from Times Square.
Sessions also emphasized the need to attract centrists and independents to defeat Clinton, whom he predicted will be the Democrats' candidate. He said the election would be a choice between the "center-right" Giuliani and Clinton, whom conservatives "are really fearful of."
Thompson pollster John McLaughlin said he thinks conservative support for Giuliani will fade as people learn more about his moderate views.
"As voters realize they're better off with Fred Thompson as a true conservative, Giuliani's going to lose votes to us," McLaughlin said.
The three AP-Ipsos polls were conducted Oct. 1-3, Sept. 21-25 and Sept. 10-12, and involved telephone interviews with a combined 1,144 Republicans and Republican leaners. The margin of sampling error for all Republicans was plus or minus 2.9 percentage points.