Sen. John Thune may have just been elected Senate Republican Conference chairman in January, but he is still eyeing a move up the leadership ladder this year with either a run for Whip or for National Republican Senatorial Committee chairman.

When asked Tuesday about his plans to pursue either position this fall, the South Dakota Republican said: “I haven’t ruled any options in or out. We’ll make a determination at some point, probably after the election.”

That would give him precious little time to mount an insurgent campaign for Whip against current NRSC Chairman John Cornyn (Texas) because the secret-ballot leadership elections for both parties generally take place within two weeks of the elections.

Still, Thune said he is in “no rush to decide anything right now” and is focused on his current job as Conference chairman, which he said he enjoys.  

“I’ve got a job right now,” Thune continued. “I want to do the best with that. I obviously want to help my team in the fall elections — help elect more Republicans to the Senate.”     

The NRSC position might end up being the more attractive post for Thune, who is known to harbor national ambitions and has been mentioned as a possible, though unlikely, running mate for presumptive GOP presidential nominee Mitt Romney.

“What you do is develop a national political network,” a GOP Senate aide said. “There are few posts that give you a chance to develop political relationships across the country.”

Aides said the NRSC chairman position may also be appealing next cycle because, similar to the current cycle, there are fewer Republican seats to defend. In 2014, there are 20 Democratic seats up for re-election, while there are only 13 Republican seats up.

The GOP will be looking at possible pickups in West Virginia, South Dakota, Alaska and Montana, as well as possibly New Jersey, the aide said.

“The next cycle offers a real opportunity to win and have a real impact,” the aide added. “It’s not every cycle that you have to defend fewer seats than Democrats.”

Currently, Cornyn is the only candidate for the Whip post, which is being vacated at the end of this year by retiring Sen. Jon Kyl (Ariz.).

The Texas Republican said that while he hasn’t given the Whip race much thought lately, he does expect a challenger.

“I anticipate there will be because I don’t take anything for granted,” Cornyn said.

“My personal goal has been to find a way to advance the causes I believe in, and if I am given an opportunity to do that as Whip, I would be grateful,” Cornyn continued.

Republicans hold 47 votes in the Senate, and if they were to win the majority, that could further boost Cornyn’s candidacy for Whip. After all, the NRSC chairman would be given much of the credit for electing more Republicans to the Senate.

“I think people will [at least] be in a better mood,” Cornyn said of the scenario.

But some Senate GOP aides said a good day at the polls in November might not necessarily translate into a win for Cornyn if Thune enters the Whip race because lawmakers already expect to at least gain seats, if not win the majority, based on what they see as favorable tail winds in competitive states across the country.

“Cornyn is the leading contender and has a compelling case to make, but not necessarily because Senators feel they owe him something,” another GOP aide said.

Cornyn took the helm of the NRSC after the disastrous 2008 cycle — a moment when the job had few takers and 2010 looked to deliver Republicans another shellacking. But 2010 turned out to be a wave election for the GOP, with Cornyn earning plaudits for his management of the NRSC.

Both Thune and Cornyn are reasonably well-liked in the GOP Conference.

“If [Thune] did [enter the Whip race], then he would garner a lot of support because there are a lot of people who think highly of him, and I think he is an integral part of leadership,” Sen. Richard Burr (N.C.) said. Burr briefly threw his hat in the ring for Whip, but he backed out after deciding his policy and legislative goals were incompatible with running for and serving in a leadership position.

“But in races like this, as people have seen for years, the person who is in it early tends to lock down the vote,” Burr said.

Nevertheless, he said Thune would be a formidable opponent.

“But it is a private vote, so somebody like John Thune has the capability to move folks,” Burr said.

A race between the two would also be difficult for the Conference, with hard feelings likely to result.

“It’s a Senator’s least favorite task to pick among two peers,” said a Senate Republican aide, who added that the Conference could opt to work out an agreement where Cornyn is chosen as Whip and Thune is made NRSC chairman.