Story highlights President Obama said Gadhafi's death made it a "momentous day in the history of Libya"

Authors say the demise of Gadhafi won't greatly boost Obama's re-election chances

They say Americans are focused on domestic, not foreign policy, concerns

Authors: Obama can argue that he wields force more prudently and surgically than Bush

With Libyan dictator Moammar Gadhafi's dramatic demise this Thursday morning, the world is rid of a tyrant, and a free Libya has jumped a mile forward to stability (though, as CNN's Ben Wedeman reports , there are still many more miles to go).

Yet in America, we are speeding toward the 2012 presidential elections, and talk quickly turns to the political considerations here. President Obama appeared Thursday afternoon in the White House Rose Garden to celebrate this "momentous day in the history of Libya" and to declare that "one of the world's longest dictators is no more."

As Obama pledged his support to Libya's future, many in the crowd and watching at home surely began to wonder about the president's own future. It is a much-discussed irony that a president elected largely around domestic concerns has gone on to amass some sterling foreign policy bona fides, while his approval on matters stateside sinks deeper and deeper. But what impact, if any, will his string of overseas successes have on his standing -- and re-election prospects -- here at home?

The first, most obvious answer is: not much. While you might expect a president who has bagged Osama bin Laden, Anwar al-Awlaki, and now Moammar Gadhafi in just under six months to be riding high in the public's estimation, foreign policy concerns simply don't register much on the public's radar these days. With the economy sputtering -- and veering dangerously toward the edge of another downturn -- voters are homed in there. An October Gallup poll found 32% mentioning "unemployment/jobs" as the most important issue facing the nation, with another 31% mentioning "the economy in general." Where did "wars/fear of war" and "terrorism" stack up? Two percent each.

David Gergen

Nor does it help that Libya was never a particularly popular war in the first place. A March Gallup poll taken just one day after our Air Force began helping enforce the no-fly zone over Libya showed Americans approving of our involvement, 47% to 37% -- a majority, yes, but lower than every other foreign military action since Vietnam (including Grenada and Kosovo). Critics may likewise downplay how much credit the president deserves for Gadhafi's demise -- after all, there's no indication American forces took him out, the way they got al-Awlaki and, unforgettably, bin Laden.

Nevertheless, there may be some political benefits in this string of successes for Obama: Even if they don't lift his approval up to dazzling heights, they fortify him against criticism on the foreign policy flank and give courage to his remaining supporters. The victories may also help firm up the president's standing as a decisive leader, a contrast that may prove helpful if he faces former Massachusetts Gov. Mitt Romney -- whom rivals on both sides of the aisle like to portray as changing with the wind -- in the general election.

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Defense Secretary Bob Gates said in September that Obama's decision to go after bin Laden with Navy SEALs was one of the most courageous ever made by any of the eight presidents he has served -- and Obama's gamble on Libya (derided by critics quoting the characterization of "leading from behind") certainly seems to be paying off as well. His approach (later redubbed by the publication that first reported it, " leading from behind the scenes ") will also bolster a campaign argument that may resonate not only with his base, but also with swing voters increasingly wary of foreign engagements: that Obama wields force much more prudently and surgically than the reckless GOP -- that he has wound down Iraq and helped win back international respect, all while delivering strong results.

Still, domestic issues reign supreme, and so it's hard to say that the credit Obama will get for these successes abroad will be enough to turn back the tide of his sinking poll numbers. An August NBC/Wall Street Journal poll found Obama's approval on foreign policy a positive 50% to 45%, but the same poll gave him horrendous 37% to 59% marks on the economy and a 44% to 51% disapproval overall. Since then, he's only slipped, with the latest Gallup tracking poll putting his total approval at 39% to 54%.

Obama may yet get a bump from the Gadhafi news, but it's hard to imagine it overshadowing the bin Laden spike, which itself proved extraordinarily fleeting. In the meantime, if he wants to bring the numbers back up for the long haul, the president will have to find a way to transfer some of that daring success of his War Room into his domestic Cabinet.

In their second terms, presidents often find themselves drifting into more and more foreign policy initiatives, both as a way to bolster their legacies and because they find that, with their domestic political capital usually spent, it's the only arena left where they can make a big impact. Obama has gone through that cycle a bit quicker than most, and it leaves one questioning what his second term would look like.

Whether or not that comes to pass, he will at the very least be able to console himself that even if the voters aren't rushing to record these international victories, the history books one day will.