In a Pew Research poll released earlier this month, 53 percent said they would blame the GOP if the crisis was not resolved, versus just 27 percent who said they would blame Democrats.
But Boehner has also lost favor with some conservatives after removing four Tea Party freshmen from their preferred committees for breaking with leadership on key votes. That's led to some Republicans suggesting that Boehner could be vulnerable in a vote to retain his gavel next month.
Earlier Friday, Rep. Nan Hayworth (R-N.Y.) said Friday that she has "every bit of faith" in Boehner despite having failed on the "Plan B" vote.
"He's really trying to do the best he can, under the circumstances, for the American people," Hayworth said on CNN's "Starting Point." "I have great confidence in the Speaker's ability to navigate very, very difficult waters in policy and politics."
More from The Hill:
• Fearing primaries, GOP members opted to shun 'Plan B'
• Boehner challenges Obama, Democrats to act on 'cliff'
• Obama commemorates service members for the holidays
• Conservatives urge GOP to prepare to go over cliff
• TSA prepares for Christmas — and holiday terror threats
• CIA: 'Zero Dark Thirty' is 'not a documentary'