“There’s a real concern that there’s between 30 and 40 people that would vote against the speaker on the House floor, so they’re trying to change the conference rules to make sure that doesn’t happen,” said a GOP member familiar with the proposal.

At the same, time, according to sources, conservative lawmakers are discussing something of a counter-proposal. Under their plan, the November leadership elections would be pushed back until after the lame-duck session of Congress ends in December. This idea was described by one House conservative as a preemptive strike to warn leadership not to consider any significant legislation during the 15-day “lame-duck” period between November’s midterm elections and the start of the new Congress.

This proposal, in light of the proposed pelaties for voting against the speaker in January, could also be aimed at giving a challenger additional time to organize supporters for the conference elections.