While more conservative GOP lawmakers in the House celebrated the decision of Speaker John Boehner to leave his post, those same Tea Party lawmakers readily acknowledged that they are passing on the idea of trying to elect one of their own fellow conservatives as Boehner's replacement, or even to fill another expected opening for a top Republican leadership post in the House.

"This has never been about making the conservatives the leaders of the party," said Rep. Raul Labrador (R-ID).

"We never thought we had enough votes to get one of our own elected," said Rep. Mick Mulvaney (R-SC), as he and other conservatives argue the basic plan is to force change within the GOP, not seize the Speaker's job.

"The goal is to try to improve the process, and improve the system," Mulvaney told me.

"That wasn't my goal," said Rep. Ted Yoho (R-FL), when asked why conservatives weren't in the race for Speaker; Yoho wants fellow conservatives to quiz leadership candidates on what they would do if elected as Speaker.

"I think it is important that we have a set of principles that we believe in," said Labrador.

The strategy of not running anyone for Speaker - but trying to play kingmaker - could result in a situation where more conservative Republicans withhold their votes on the House floor, and keep a GOP candidate short of the majority needed to win an election as Speaker.

"We've got a block of votes from people who are saying we need changes," said Rep. Tim Huelskamp (R-KS).

"No one has 218 votes today," Huelskamp told reporters off the House floor.

At this point, there are only two candidates running for Speaker - Majority Leader Kevin McCarthy (R-CA) and Rep. Dan Webster (R-FL).

"My whole message is that I want to have a principle based, member driven Congress," said Webster, whom I ran into as he went into a meeting in McCarthy's Capitol office.

Before returning to Washington earlier in the day, Webster had been working the phones for support, urging his fellow lawmakers from Florida to jump on board with his effort.

Not everyone was rushing to join him.

"I'm not going to play my hand right now," said Yoho, when asked if he would back his home state colleague. "Dan is a great friend of mine."

Republicans will meet on Tuesday evening at the Capitol for a members-only discussion of where the leadership fight will go.

While it wasn't clear when the GOP leadership elections would be set in October, it was obvious that many candidates were doing all they could to win support, not only in the race for Speaker.

Just off the House floor, GOP Whip Steve Scalise (R-LA) was feeding supporters Greek food while pressing for support in his bid for Majority Leader.

There was Rep. Tom Price (R-GA), keeping close tabs on his own vote cards, shaking hands and chatting other lawmakers on the House floor.

"We're talking to a lot of people," Price said as he walked past reporters.

On the floor, Tea Party Rep. Tom Massie (R-KY) was in demand; he sat for a lengthy chat with Webster, and then shuttled across the floor to talk to Price.

A ways over was Rep. Markwayne Mullin (R-OK), ready to run for Whip; "he's a viable candidate" one Republican told me, arguing the GOP was about to go through a major turnover.

In the midst of all the personal lobbying for the leadership races, a very relaxed looking Speaker Boehner came off the floor and walked through the Speaker's Lobby.

Boehner greeted me by name and gave me a hearty handshake, then made his way toward the door, stopping to exchange playful greetings with a couple of fellow lawmakers.

Reporters didn't give chase to Boehner for any comment on what was happening around him - more focused on the race for someone to replace the Speaker, who plans to leave Congress on October 30.