Multiple House Republicans — some who voted for Boehner in 2013 and some who didn’t — praised Hensarling as a solid conservative, but also told CNN there’s a short list of others who are viable candidates.

Many House Republicans interviewed by CNN declined to talk openly about potential leadership challenges, but admitted there are informal discussions about options.

The names repeatedly raised include Ohio Republican Jim Jordan, who like Hensarling is a former chairman of the fiscally conservative Republican Study Committee; Louisiana Republican Rep. Steve Scalise, who currently heads that group; and Georgia Rep. Tom Price, another former study group leader who also served in Boehner’s leadership team in the last Congress.

“The one consensus point is that we’d like to see more conservatives in future leadership posts,” Louisiana Republican John Fleming told CNN.