A new poll shows President Barack Obama’s disapproval rate among political independents has broken above 50 percent, even while he is using the debt ceiling debate to seek approval from those critical swing voters.

Support for Obama among independents has fallen from 42 percent in May to 31 percent, and disapproval has risen to 54 percent, according to a late July poll of 1,500 registered voters by the Pew Research Center for the People & the Press.

The drop in support among independents is critical because both parties have a roughly similar number of die-hard supporters. The 2012 election prize will go to the candidate who draws more independent voters, and Obama’s decline in that crucial demographic has dragged his ratings down among registered voters, according to the Pew poll.

“The sizeable lead Barack Obama held over a generic Republican opponent in polls conducted earlier this year has vanished,” Pew announced today. “Currently, 41% of registered voters say they would like to see Obama reelected, while 40% say they would prefer to see a Republican candidate win in 2012.  In May, Obama held an 11-point lead.”

Much of that decline is due to the stalled economy.

But Obama’s losses among independent voters are especially stinging because he has used the debt ceiling debate to showcase his compromiser-in-chief role to independents, while also trying to maintain his support among progressives. (RELATED: Polls indicate economy hurting Obama)

To win the independents, Obama has reversed his support for high-spending policies, and now says he wants curbs on spending and cuts to entitlement programs. He has also publicly portrayed himself as the even-handed arbiter between Democrats and Republicans, and as a White House consensus builder in a gridlocked Washington.

That’s a difficult task, partly because he has refused to reveal the details of his budget preferences, and partly because those details would cost him support among his left-wing supporters. In recent days, reporters have repeatedly asked White House spokesman Jay Carney for the details of Obama’s proposals, but Carney has declined to reveal any.

Carney did imply, however, that the president’s stance in the debt-ceiling negotiations is a popular one and is boosting his clout. The White House press secretary insisted today that “we’re winning this argument on the merits, as a political matter.”