Instead of using the resignation of Speaker John Boehner as a springboard for a leadership shakeup, more conservative Republican lawmakers in Congress are struggling to find any candidate that they can rally behind, leaving them on the sidelines during this major leadership scramble.

"This is a very critical time," said Rep. Barry Loudermilk (R-GA), who readily acknowledged the lack of conservative candidates for GOP leadership posts in the House.

"I haven't heard of any that are going to stand up and run," Loudermilk told me, as the freshman Republican indicated that he's not ready to endorse anyone yet in the race for Speaker.

Evidence of the disappointment of conservatives was on full display Tuesday, as some GOP lawmakers tried to publicly push Rep. Trey Gowdy (R-SC) into the race for House Majority Leader, arguing he would be the perfect candidate to stress conservative political principles.

"When it comes to making the case, there's nobody better than Trey Gowdy," said Rep. Jason Chaffetz (R-UT), who joined several other Republicans in trying to draw Gowdy into the race for the number two GOP leadership position.

But after a few hours of such talk, Gowdy told reporters that he would not join that leadership race, again leaving more conservative Republicans disappointed.

It was yet another development that left some Republicans grumbling about their options, unexcited about Rep. Kevin McCarthy's likely ascension to the job of Speaker.

"Kevin certainly is no conservative," said Rep. Mick Mulvaney (R-SC), a leading member of the House Freedom Caucus said of the Majority Leader. "Kevin is not a member of our group."

But for now, McCarthy is the solid favorite for Speaker, as only one other candidate has joined that race, Rep. Dan Webster (R-FL); Webster is considered a long shot.

"Dan is a good guy," said Rep. John Mica (R-FL), "but he isn't as well known."

McCarthy seemed to be solidifying his support on Tuesday, nailing down endorsements from prominent Republicans like Rep. Paul Ryan (R-WI).

"At this critical moment, Kevin McCarthy is the right person to lead the House of Representatives," Ryan said of the Majority Leader, who was confidently making the rounds on TV.

Republicans met behind closed doors on Tuesday evening to discuss what's next in the leadership race, a meeting that some described as a chance to vent their frustrations.

"There needs to be a major therapy session and a lot of dialogue and a lot of putting down our knives and just having a really great heart-to-heart and coming to grips with some very, very, tough things," said Rep. Matt Salmon (R-AZ), who has demanded major change in how the House operates.

No decision was made on when the leadership elections would take place.

"I would hope to make an announcement in the next day or two about that," said Speaker Boehner, who did not attend the evening gathering of Republicans to discuss how he would be replaced.