The GOP factionalism could become even more significant this fall when it’s time to cut deals with Senate Majority Leader Harry Reid (D-Nev.) and the White House on boosting the debt ceiling and keeping the government operating past September. McCain, Corker and other members of the “Supper Club” — a group of Republicans who have been discussing budget issues with White House Chief of Staff Denis McDonough — met with McConnell on Thursday afternoon, seeking strategies for those looming fiscal showdowns, which will really kick off in September.

McCain wants to see Senate Republicans negotiate with Democrats on these critical matters, but there are a number of GOP conservatives — especially in the House — who are prepared to shut down the government or default on the debt unless Obama caves to their spending demands…

Democrats have been trying to exploit these fissures, especially during the nuclear option standoff. Reid was able to reach out to McCain — who had already been negotiating with Sen. Chuck Schumer (D-N.Y.) — in order to round up GOP votes to overcome Republican filibusters against Obama nominees.

Not all Republicans were happy with the deal. Sen. Kelly Ayotte (R-N.H.) was stunned Thursday that Republicans had allowed Labor secretary nominee Tom Perez to be confirmed, claiming his confirmation was “not part of the nuclear option deal.” Other GOP senators insisted he was.

And a number of Republicans were angry that the deal allowed Cordray to be confirmed without changes to the consumer agency that the GOP had long demanded as a condition for his confirmation.