Despite running third behind Hillary Clinton and Barack Obama in every national poll to become the Democratic presidential nominee, John Edwards has emerged as the only candidate poised thus far to defeat leading GOP contender, Rudy Giuliani.

Earlier this week, SurveyUSA released polls in 11 states of head-to-head candidate matchups between Giuliani and each of these three Democratic Party frontrunners. The eleven states surveyed in mid-April included 6 that went to George W. Bush in 2004 (Iowa, Kentucky, Missouri, New Mexico, Ohio, and Virginia) and 5 that were carried by John Kerry (California, Massachusetts, Minnesota, New York, and Wisconsin).

John Edwards leads Giuliani in an early hypothetical matchup in 9 of these 11 states—only trailing the former New York City mayor in his home state of New York (by just 5 points) and New Mexico (by 3 points, within the margin of error). Edwards’ average advantage over Giuliani in the 9 other states is 7 points, including double digit leads in the battleground states of Iowa (+10) and Wisconsin (+14). Edwards’ lead was within the margin of error in only two of these states: Massachusetts (+1) and Kentucky (+3).

Hillary Clinton, however, has fallen behind Giuliani in 6 of the 11 states, trailing in Virginia (-5) and 5 states within the margin of error: Wisconsin (-1), Kentucky (-2), New Mexico (-2), Iowa (-3), and Missouri (-3). Clinton has opened up double digit leads in California (+12), Massachusetts (+12), and the battle for New York (+11).

Barack Obama emerges as the least competitive of the “Big 3″—leading Giuliani in only 2 states: Iowa (+5) and California (+1, within the margin of error). Obama trails Giuliani by an average of 9 points in the remaining 9 states, with only one within the margin of error (Wisconsin, by 2 points). Obama is looking up at double-digit deficits in four key states that all went Republican in the 2004 presidential race: Kentucky (-16), Virginia (-15), Ohio (-11), and New Mexico (-10).

To this point, Edwards clearly has the advantage in terms of “electability” versus the powerhouse Giuliani. Whether or not the Democratic base takes this into consideration when picking their nominee next year is an open question.