Speaker John A. Boehner, R-Ohio, is heading into the lame-duck session and the 113th Congress knowing full well that the road ahead is going to be bumpy. Wednesday will give an early indication of just how treacherous it will be.

The leadership election to become GOP Conference chairman might serve as the first indication of who has the heart and soul of the conference. Conference Vice Chairwoman Cathy McMorris Rodgers of Washington is vying for the spot against Tom Price of Georgia, the Republican Policy Committee chairman.

Although Boehner has remained neutral publicly, it has been no secret that leaders have supported McMorris Rodgers, a loyal Boehner ally and a reliable vote for leadership’s priorities. If Boehner’s preferred candidate cannot hold the line, the prospect that the speaker can sway his conference into accepting a bargain in the upcoming leadership elections might also dim.

The battle has been described by aides as one between mainstream and leadership-friendly Republicans, represented by McMorris Rodgers, and more hard-line conservatives, many of whom are members of the Republican Study Committee, which Price used to chair.

Boehner did try to avoid the fight. As Buzzfeed reported last week, he offered Price, who has at times bucked party leaders, a different spot at the leadership table if he dropped the bid and pledged to vote along with leadership for the next two years.

Price declined, and the race will likely remain neck and neck until members cast their ballots Wednesday afternoon.

New members arriving for orientation said Tuesday they had been lobbied hard for their votes.

When asked whether the camps had contacted him, Rep.-elect Kevin Cramer, R-N.D., said: “Oh, boy, have they ever. They started near as I could tell courting us a little before the election with checks. I’ve known a lot of them for a long time. I was a Young Gun, part of that program, so a lot of those folks were participating and were very generous early on. Since then, of course, they’ve called, they’ve emailed, sent packets. It’s been a week of politicking, which is kind of fun. Here you come off of one campaign, you go on another.”

Cramer was leaning toward Price.

In another indication of the stakes, House Budget Chairman Paul D. Ryan of Wisconsin, GOP presidential contender Mitt Romney’s running mate in his failed race against President Barack Obama, broke with Boehner on Tuesday and wrote a letter to colleagues offering his support for Price.

“No one will work harder than Congressman Price at building a strong and compelling communications and policy strategy that reflects the will of our membership and the needs of the nation,” Ryan wrote.

If Price does best McMorris Rodgers, it would show that Ryan’s influence might outweigh that of his own party leaders. That comes as he seeks a waiver to stay past his term limit as chairman of the Budget Committee, where he could drive the discussion about taxes and spending in the lame-duck session — possibly further to the right than what leadership wants.

Although Ryan had pledged his support to Price before being drafted onto the presidential ticket, the public endorsement now comes with some awkwardness. McMorris Rodgers was a top congressional liaison for the failed presidential bid, and there was some expectation that although Ryan had already pledged support for Price, he would stay out of the campaign when or if he returned to Capitol Hill.

“Everything that the congresswoman did for the Romney-Ryan ticket, and then to think this is Ryan’s way of saying, ‘Thank you,’ for going to all the battleground states and putting in work for him,” said a source familiar with McMorris Rodgers’ campaign.

The campaign has held a meeting with members who are whipping up support for her and has been working the phones to ensure that the letter from Ryan hasn’t lured any rank-and-file members out of her corner.

They are also more actively pushing the idea that it would be beneficial for the party to have a woman in a top leadership spot, particularly after Republicans lost big in that demographic on Election Day.

If McMorris Rodgers proves successful in her bid, it might indicate a Republican Conference more willing to help its leadership along, especially in a climate where everyone acknowledges that leaders will have to work with Democrats to pass any substantive legislation.

Still, for all the uncertainty about who will become the fourth-ranking GOP leader, a direct challenge to Boehner is off the table, several sources said. Notwithstanding recent griping from a few members about the public posture Boehner has taken in negotiations with the White House over the fiscal cliff, Boehner is certain to retain the speakership.

Even Rep. John Fleming, R-La., who publicly questioned the speaker’s comments about immigration reform and allowing revenue as part of a deficit bargain, said he sees no chance that he will be seriously challenged. “It’s always possible someone would challenge him, but I wouldn’t see that as successful,” he said.

The days also seem to be gone when speculation about whether Majority Leader Eric Cantor, R-Va., or even perhaps Ryan himself, would try to wrest the gavel from Boehner, according to several sources.

“I think that could have worked if we lost, let’s say, 20 seats in the House,” said one conservative aide. “There’s no outrage out there against Boehner. People think the problems are elsewhere.”

Emma Dumain contributed to this report.