WASHINGTON — Tom Graves can neither confirm nor deny that he is being vetted as Mitt Romney’s running mate.

Speculation has reached an absurd level with the notion that the 1 1/2 term congressman from Ranger could be vice president. The idea was pitched on the radio by Graves’ ebullient constituent, Ellijay activist Joe McCutchen. It became a Web report, which was mass-distributed by Graves’ press office, leading to a debate on the subject on the well-trafficked Peach Pundit blog.

Thus, in between House votes last week, Graves played the coy part of a real contender and told The Atlanta Journal-Constitution he was not interested in discussing whether he had been in touch with Team Romney or his interest in the job.

The vice-presidential speculation is far-fetched, but there’s a very real chance that Graves and two other Georgia Republican House members may jump into the chamber’s leadership hierarchy next year — moves that, in tandem, could give the state serious clout if the House remains in Republican hands.

Graves has been approached about leading the Republican Study Committee — effectively the right wing of the House GOP and incubator of the most aggressive conservative policymaking. Roswell’s Tom Price has a shot to move up one rung in the leadership ladder to Republican Conference chair, the fourth-ranking spot. Coweta County’s Lynn Westmoreland is considering a bid to head the National Republican Congressional Committee.

All three are mostly reluctant to talk about those potential contests. First off, they have to defend their own seats. Two Democrats are vying for the chance to take on Price, Westmoreland has a pair of Republican primary challengers, and Graves has a Democratic foe.

Aside from their own races, the trio must remain focused publicly on the task of electing Romney and down-ballot Republicans.

The outcome will dramatically shape the jobs the Georgians might seek. Take the NRCC, which Westmoreland says he is still deciding whether he wants to lead after having been a lieutenant on the committee, working mostly on redistricting and candidate recruitment. If Romney is elected, the NRCC chairmanship will become a much more difficult job, as the party holding the White House almost always loses seats in Congress in the midterms.

If Republicans lose control of the House — a slim possibility — the speakership will go to the Democrats, and the number of official GOP leadership positions shrinks. It then becomes a game of musical chairs that Price might not opt to play.

Price was asked directly on CSPAN last week why he would make a better Republican Conference chair than his likely rival, Rep. Cathy McMorris Rodgers of Washington state. In addition to the standard answer about being focused on this fall, Price added: “These races aren’t run in the press. These are races that are within the conference.”

Indeed, the contests are held outside of public view, with members leveraging their personal connections, ideas for the position, accomplishments and generosity with campaign cash to their fellow members.

Sometimes the contests are settled without divisive campaigns. Westmoreland indicated in a recent interview that the possible NRCC hopefuls would sit down sometime in the next few months and hammer out who would be best for the job. In Graves’ case, the next RSC chair is typically anointed by the founders and past leaders of the group — which include Price. Graves, too, was not ready to lobby for the post in public.

“We’re focused on doing our job here,” he said. “It’s up to the RSC to decide who the next chairman is.”

It was a positively vice-presidential answer.