A House Republican panel huddled in the basement of the Capitol on Monday to discuss who will wield the gavels on several committees in the next Congress.

Fox News was told the most prominent committee chairs to be decided are for the Ways and Means and Oversight committees. The decisions to formally tap the chairs were originally scheduled for Monday, but were delayed until Tuesday after some members were unable to make it in due to bad weather.

For Ways and Means, Chairman Dave Camp, R-Mich., is retiring. Current House Budget Committee Chairman Paul Ryan, R-Wis., is the odds-on favorite to grab the Ways and Means gavel, though is facing a challenge from Joint Economic Committee Chairman Kevin Brady, R-Texas.

It is notable that on Friday, the House Republican Conference voted to establish what some are now calling the “Paul Ryan Rule.” That rule would ban sitting committee chairs and the chairs of appropriations subcommittees from seeking other offices – if Ryan is selected, it would bar the former vice presidential nominee from both holding the chairmanship and running for president in 2016.  

The other big chairmanship up is for the Oversight Committee. Current House Oversight Committee Chairman Darrell Issa, R-Calif., is term-limited in that role. The main contenders are Reps. Jason Chaffetz, R-Utah; Mike Turner, R-Ohio; and Jim Jordan, R-Ohio.

Chaffetz has worked hard to garner support for the role. In addition, at hearings over the recess on Ebola and the Secret Service, Issa seemingly handed off the gavel to Chaffetz to chair portions of the hearing when he left the dais.

But House Speaker John Boehner, R-Ohio, wields a lot of influence on the Steering Committee, which decides these posts. And it’s possible he could draft one of his Buckeye State colleagues over Chaffetz. Both Turner and Jordan hold seniority in Congress over Chaffetz – and Turner’s district abuts Boehner’s.