Sen. Richard Burr (N.C.) is the new underdog in the race for Republican Whip, having displaced Sen. Lamar Alexander (Tenn.) as Sen. John Cornyn’s foil in the Texan’s bid for the No. 2 GOP leadership post.

Cornyn is chairman of the National Republican Senatorial Committee for the second consecutive cycle, and he is expected to benefit from helping lead his Conference from a low point of 40 Members in 2009 — not even enough to mount a filibuster — to, possibly, the majority, depending on the outcome of the November elections. Still, Burr’s strength could be the depth of his personal relationships with many in his Conference — connections he has nurtured as Chief Deputy Whip. GOP Senators will vote on their slate of leaders in the weeks after the general election.

“It’s Cornyn’s race to lose,” a knowledgeable GOP operative said Tuesday. But the operative cautioned against dismissing North Carolina’s senior Senator, describing him as “formidable.”

Burr, who entered the Whip race late last year after Alexander decided to exit both the Whip race and leadership altogether, appears to agree that Cornyn is the favorite. “He’s got the inside track,” Burr said. “He serves in the leadership and has done a good job at the NRSC.”

Senate Minority Whip Jon Kyl (R-Ariz.) is retiring, opening the Whip slot beginning in the 113th Congress. Cornyn and Alexander — then the No. 3 Republican as GOP Conference chairman — announced their bids to succeed Kyl about a year ago, around the same time the Arizonan revealed he would not run for re-election in 2012. Cornyn was viewed as the leading contender in that two-man race as well. But by October, Alexander was out and Burr was in.

Cornyn has the advantage at least partly because he has been campaigning longer and probably has committed supporters lined up. Of course, Senators have been known to promise their votes to one candidate and then vote differently in these secret-ballot leadership elections. But the campaigning has been relatively quiet following an admonition in early 2011 from some GOP Members that the Conference could ill afford to be distracted by internal divisions — particularly with the Senate majority within reach.

Since those warnings were issued, overt campaigning has been at a minimum save for the occasional low-level conversation, according to a Republican Senator who has discussed the Whip race with the candidates. Cornyn agreed that the campaigning has been on a “hiatus” but indicated he is prepared to run aggressively when the time comes.

“By the time the race happens, after four years of chairman of the NRSC, I’ll look forward to a new job where I can continue to contribute to our Conference,” Cornyn said, adding: “Richard’s a very good Senator. I certainly don’t take anybody’s vote for granted.”

The contest is expected to heat up this summer and remain active through Election Day and beyond. The voting will be restricted to Republicans who will take office in January 2013 and will include those elected this year. Sen. John Thune (S.D.), who succeeded Alexander as Conference chairman, has not ruled out joining the Whip race. But Cornyn is projected to remain the frontrunner, barring an unforeseen change in the dynamics of the race.

Cornyn took the helm of the NRSC following the disastrous 2008 cycle — a moment when the job had few takers and 2010 was predicted to deliver Republicans another shellacking. But 2010 turned out to be a wave election for Republicans, with Cornyn earning plaudits for his management of the NRSC. If Republicans capture the four seats needed to win the Senate majority, Cornyn is thought to be a lock for Whip.

Even if the GOP comes up short, Cornyn could still be an overwhelming favorite. Republican operatives say the view in the Conference is that Cornyn has worked extremely hard during his time at the NRSC and delivered tangible benefits to Members. An individual who works hard and produces results are qualities Republicans value when electing leaders — sometimes more than personal relationships.

“Cornyn has done so much for the Conference. Even if Republicans don’t win the majority, they would likely blame it on presidential head winds,” a former Senate GOP leadership aide said. “Burr has a lower profile from which to operate on.”

Still, Burr doesn’t come to the table empty-handed.

His work as Chief Deputy Whip under Kyl, while rarely a launching point into senior leadership, has prepared him for the job and given him an opportunity to interact with Members on a daily basis. The North Carolinian has been on Capitol Hill longer than Cornyn, and he has forged closer ties with several Members, particularly those with whom he served in the House.

Critics of Cornyn have described his relationships with Members as “a mile wide and an inch deep.”

“Burr is a more social Member and has more real friends,” and there is more intensity behind his relationships, a Republican lobbyist said.

If Burr does lose the Whip race, some Republicans believe he could end up as the next NRSC chairman.