Former Massachusetts Gov. Mitt Romney (R) stressed Tuesday that he doesn't care about the politics of Osama bin Laden's killing this past weekend.

But that doesn't mean President Obama's unbeatable in 2012, the GOP heavyweight said.

"I think the killing of Osama bin Laden is an enormous success, and I don't know if it helps or hurts the president politically, but I really don't care," Romney told reporters in New Hampshire, the host of the first-in-the-nation primary, according to video captured by NECN.

"The right thing is we got the bad guy, and the nation celebrates that," Romney added. "We’re all Americans. This is not a Republican or a Democrat thing; this is an American thing.”

Romney, arguably one of the top contenders for the Republican nomination to face off against Obama in 2012, sought not to politicize bin Laden's slaying at the hands of U.S. special operations forces in Pakistan on Sunday in a mission ordered by Obama.

A number of Republicans have awarded praise for the president in the aftermath of the operation. Romney said that Obama certainly "deserves credit" for the mission, particularly for approving the high-risk strike against bin Laden's compound.

"The bad guy took one in the eye," Romney said of the attack.

But the Republicans are also beginning to emphasize, two days after the initial attack, that there are limits to the political capital Obama stands to collect as a result of the operation.

"I don't think so," Romney said when asked if Obama was unbeatable in 2012.

Obama received a small bump in his approval rating on Tuesday in the aftermath of the assault against bin Laden. His favorable ratings on his handling of the situation in Afghanistan and the general war on terror enjoyed a particularly healthy bounce.

Another top Republican contender for the nomination, former Minnesota Gov. Tim Pawlenty (R), stressed that Obama's overall foreign policy record is still subject to Republcians' scrutiny.

"President Obama should be congratulated for his commitment and decision-making in the capture of bin Laden,” Pawlenty said in Iowa. "But that’s not the full scope of our foreign policy or our national defense posture and there will still be a robust debate about what he has done so far and what he will do in the future."