As the U.S. approaches a possible debt default in the next couple of months, Republican leaders say they have the edge to get President Obama to agree to significant spending cuts. "We have to use whatever leverage we have," Senate Minority Leader Mitch McConnell (R-Ky.) recently said. "The debt ceiling is one of them that hopefully would get the president engaged." However, new polls suggest that the GOP may want to think twice before it tries to strong-arm the president: Voters overwhelmingly disapprove of the GOP's handling of the fiscal-cliff talks.

According to a poll conducted by Pew, 48 percent of Americans approved of Obama's approach to the negotiations that resulted in an extension of the Bush tax cuts for all but the wealthiest Americans, while 40 percent disapproved. In contrast, a whopping 66 percent of voters disapproved of the performance of Republican leaders, compared with a paltry 19 percent who approved.

Granted, one major reason Republicans got such low marks is that members of their own party were unhappy with a deal that included a tax hike for the rich, but no spending cuts. However, in a worrisome sign for the GOP, independents were especially unhappy with Republican leaders, with 69 percent disapproving of their performance, and only 14 percent approving.

An ABC News/Washington Post poll released this week for the most part backed up Pew's findings. Obama won majority approval, 52-37, while House Speaker John Boehner's (R-Ohio) numbers were upside down, 31-51.

There is some debate over whether Republicans in the House even care about public approval ratings, given that many members benefit from gerrymandered districting that makes them immune to challenges from the center of the political spectrum. But Senate Republicans can't like what they see: Even though almost all of them joined Obama to raise tax hikes on the wealthy, they run the risk of being tarred with the same brush as their more intransigent counterparts in the House. Ditto for national Republican leaders who want to soften the GOP's image in the wake of Obama's victory over Mitt Romney.

And it could get worse as the fight over the debt ceiling intensifies. The skirmish over the Bush tax cuts only strengthened accusations that the GOP is more concerned about protecting the wealthy than preventing tax hikes on the middle class. The GOP's goal to cut popular entitlement programs, all while threatening to hold the U.S. credit rating hostage, could tarnish the party's brand even further.