The killing of Osama bin Laden gave President Obama a moderate spike in his approval ratings, but it hasn’t convinced more registered voters to support him in 2012, according to the latest Gallup poll.

Forty-three percent of registered voters said they are more likely to vote for Obama and 40 percent said they are more likely to vote for the generic Republican presidential candidate. These numbers that are comparable to previous Gallup polls from April and February.

The finding discredits the idea that bin Laden’s killing will significantly bolster Obama’s chances in 2012. But that isn’t to say that it won’t help Obama during the campaign—the death of bin Laden gives him at least one achievement to run on. Before that, he had few successes to point to during his campaign.

However, the poll does indicate one problem for Obama. The bounce in his approval ratings came mainly from Republicans, who are the most enthusiastic about bin Laden’s death but who are highly unlikely to change their votes because of it. Democrats and independents are less impressed by the achievement, according to Gallup. While 52 Republicans said killing bin Laden was “extremely important” for the country, only 42 percent of independents and 44 percent of Democrats feel the same way.

In other words, if Obama wants to run on his bin Laden success, the people that appeals to most are ones who won’t vote for him anyway. He’ll need to come up with other achievements to stump on if he wants to win over independents and disillusioned Democrats.