The president, seeking a second four-year term, beats another potential GOP rival, Alaska Governor Sarah Palin, by six points – 48% to 42%.

In both match-ups, seven percent (7%) like some other candidate, with three percent (3%) undecided.

Palin is second only to 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.

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Just 21% of voters nationwide say Palin should run as an independent if she loses the Republican presidential nomination in 2012. Sixty-three percent (63%) say the 2008 GOP vice presidential nominee should not run as an independent. Sixteen percent (16%) are not sure.

If Romney secured the GOP nomination and Palin chose to run as an independent candidate, Obama would win the resulting three-way race with 44% of the vote. Romney is the choice of 33% of the voters under that scenario, with Palin a distant third with 16% support. Three percent (3%) like some other candidate, and four percent (4%) are undecided.

Last November, Obama defeated Republican presidential nominee John McCain by a 53% to 46% margin.

When Romney is the Republican nominee, he beats Obama among unaffiliated voters 48% to 41%. But when Palin is the GOP candidate, unaffiliated voters prefer Obama by a 47% to 41% margin.

Men prefer the Republican over Obama whether it’s Romney or Palin, while women like the president better in both match-ups. Palin continues to fare more poorly among women than her male rivals.

In a three-way race, Palin hurts Romney by drawing 28% Republican support. Romney captures 52% of the GOP vote in that scenario.

In a three way race, unaffiliated voters break 40% for the president, 39% for Romney and 14% for Palin.

Nearly one-third of Republicans (32%) say Palin should run as an independent is she fails to get the party’s nomination.

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

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 if the 2012 GOP Presidential Primary in their state was held today. 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.

In mid-May, 37% of Republican voters said their party was leaderless, but this was a major improvement from March when 68% felt that way.