On the May 13 edition of Fox Broadcasting Co.'s Fox News Sunday, Fox News contributor and NPR national political correspondent Mara Liasson asserted that former New York City mayor and Republican presidential candidate Rudy Giuliani is “trying to argue” that he is “the only one who can beat a Democratic nominee -- [Sen.] Hillary Clinton [D-NY].” Liasson added, “But I don't think the polls support that. I think the polls show that in head-to-head matchups, for whatever that's worth now, they all do.” However, while some recent polling has been less favorable to Clinton, two polls released in May show her leading not only Giuliani, but also the other top Republican candidates in head-to-head contests.

A Newsweek poll, conducted May 2-3 and released May 5, found that Clinton led Giuliani 49 percent to 46 percent -- within the poll's margin of error of 4 percentage points. The poll also found Clinton leading Sen. John McCain (R-AZ) 50 percent to 44 percent and ahead of former Massachusetts Gov. Mitt Romney (R) 57 percent to 35 percent.

Additionally, a national poll conducted by WNBC and Marist College between April 26 and May 1 found that Clinton led Giuliani 48 percent to 43 percent and led McCain 47 percent to 42 percent. That poll had a margin of error of 3.5 percentage points for questions regarding head-to-head contests.

Other recent polling has shown Clinton even with or behind Giuliani and McCain.

A Diageo/Hotline poll, conducted April 26-30, showed Clinton and McCain tied at 45 percent, while Giuliani led Clinton 47 percent to 43 percent, with both cases including “leaners.” Clinton was ahead of Romney 50 percent to 35 percent, including “leaners.” The margin of error was 3.5 percentage points.

A Quinnipiac poll conducted April 25 to May 1 showed Giuliani ahead of Clinton 49 percent to 40 percent, while McCain led Clinton 46 percent to 41 percent. The poll questions pertaining to head-to-head contests had a margin of error of 2.9 percentage points.

From the May 13 edition of Fox Broadcasting Co.'s Fox News Sunday:

LIASSON: And Rudy Giuliani is saying something very bold and challenging to the party, which is terrorism and the economy are more important than social issues, and I have the best plan for both of those.

Plus -- now, this is where I don't think he has closed the sale, but he's also trying to argue that I am the only one who can beat a Democratic nominee -- Hillary Clinton. But I don't think the polls support that. I think the polls show that in head-to-head matchups, for whatever that's worth now, they all do.

But that is the challenge for the Republican Party. Is it ready to rebrand itself by de-emphasizing the social issues and nominate a Giuliani? We don't know that yet.

WALLACE: How do you think, Bill, he handled the issue in our interview?