“John is going to try to clean the barn up as best he can,” said Rep. Charlie Dent, R-Pa. “He’s not going to clean the whole thing, but we can probably dispose of the debt ceiling. I hope we can reach a budget agreement.”

Boehner’s penchant for relying on Democrats to make up for tea party defections on legislation like a 2013 tax increase and last month’s temporary government funding bill got him in trouble with the right. There’s little they can do if he follows the same strategy on the debt limit and a budget deal.

“It is ironic how smart John Boehner’s looking,” said Rep. Kevin Cramer, R-N.D. “Frankly, all this talk of a fresh new face sounds very sweet on the surface, but we’re not electing a student council president. His stock rises with the prospects of an alternative and the steadiness of his hand, the clarity of his positions – whether you like them or not – and the fact he’s not prone to panic. It’s all looking really good right about now.”