Mr. McConnell has been more open to the idea of a short-term hike in the debt ceiling, a prospect that unsettles House Republicans who would prefer not to vote multiple times on the debt limit before they all face the electorate in November 2012. (Just 10 Republican Senate seats are up next year.)

Democrats see Mr. Boehner as being more open to new revenues — he suggested earlier in the year that tax breaks for the oil industry might be expendable — than Mr. McConnell, particularly if the revenues could be tied into a major deficit reduction package. As the leader of the House, Mr. Boehner also has more riding on the outcome than Mr. McConnell…

Since Mr. Boehner became leader of House Republicans in 2007, he and Mr. McConnell have pulled in tandem in a way that has made it difficult for Democrats to drive a wedge between House and Senate Republicans. Their inner workings have also been absent of the backbiting and staff infighting that often occurs between the offices of the two leaders.

“It is a friendly and trusting relationship, and we are not looking for ways to make ourselves look better at the expense of the other,” said Mr. McConnell, who often unobtrusively makes his way over to the speaker’s office via a relatively secluded hallway off his own suite. He joked that he followed the trail of cigarette smoke emanating from Mr. Boehner’s suite.