If America elects a woman president soon, right now her name appears to be Hillary Clinton.

In a hypothetical match-up between the two most formidable female candidates in their respective parties, Clinton defeats former Alaska Governor Sarah Palin 51% to 39%, according to a new Rasmussen Reports national telephone survey of likely U.S. voters. Seven percent (7%) prefer some other candidate.

Clinton performs better against Palin than President Obama who in a hypothetical 2012 match-up beats last year’s GOP vice presidential nominee by just six points, 48% to 42%.

Women overwhelmingly favor Clinton over Palin, 59% to 32%. Men favor the GOP ex-governor by eight points, 48% to 40%.

Palin gets 71% of the Republican vote, while Clinton captures 81% of Democrats. Voters not affiliated with either party break down almost evenly between the two candidates, giving Clinton a slight 44% to 41% edge.

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However, most voters (52%) do not think Clinton is likely to be the first woman U.S. president. Thirty percent (30%) say it’s not very likely, and 22% say it’s not at all likely.

Thirty-eight percent (38%), on the other hand, say it’s at least somewhat likely that Clinton will be the first woman elected to the White House, with 15% who think it’s very likely.

Forty-six percent (46%) of women say Clinton is at least somewhat likely to achieve this milestone versus 29% of men. Fifty-seven percent (57%) of Democrats agree, but that’s a view shared by just 23% of Republicans and 31% of unaffiliated voters.

Perhaps surprisingly, voters are almost evenly divided over whether Clinton, now serving as secretary of State, will challenge Obama for the Democratic presidential nomination in 2012. Forty-four percent (44%) say Clinton is at least somewhat likely to do so, with 18% who say it’s very likely.

Forty-six percent (46%) say Clinton is unlikely to challenge the incumbent president for their party’s nomination, including 30% who say she is not very likely to do it and 16% who say it’s not at all a possibility. Obama narrowly defeated Clinton for the Democratic presidential nomination in 2008, although the former first lady had been the early favorite to win.

Fifty percent (50%) of women believe Clinton is likely to challenge Obama, compared to 37% of men. Among Democrats, 46% say Clinton is at least somewhat likely to challenge the sitting president, while 43% say she is not very or not at all likely to do so.

Rasmussen Reports will release new favorability numbers on Clinton and what voters think of her job performance as secretary of State at noon EDT today.

Obama’s overall approval ratings as measured in the Rasmussen Reports daily Presidential Tracking Poll dropped below 50% for the first time in late July but edged back to the halfway mark on Saturday.

Palin is second only to former Massachusetts Governor Mitt Romney as the presidential candidate Republican voters say right now that they’ll vote for in 2012 state GOP primaries. But she’s also one of two candidates they least hope wins the party’s nomination.

Those who say economic and fiscal issues are their biggest concerns make up the majority of Republican voters, and Romney runs best among those voters. Palin is the top choice for those Republicans who put national security first and ties Romney for first among voters who list economic issues alone as the priority. She runs second in nearly every other case with voters from all camps.

Forty percent (40%) of Republican voters nationwide say Palin’s decision to resign as governor of Alaska hurts her chances of winning the party’s presidential nomination in 2012.

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