They have seized committee gavels and newfound political clout, but the flurry of promotions within the new Republican House majority could complicate the GOP’s plans to wrest control of the Senate from Democrats in 2012.

From New York to Ohio to Wisconsin, would-be Republican Senate candidates might prefer to hold on to new leadership posts rather than run for statewide office in the next cycle, a process that has already begun in some states.

New York Republicans have long pushed Rep. Peter King to run for the Senate, but the 10-term Member told Roll Call that he’s thrilled with his new role as chairman of the Homeland Security Committee.

“Since Sept. 12, 2001, homeland security has been my absolute focus, almost an obsession,” King said, acknowledging speculation that he will challenge Sen. Kirsten Gillibrand (D) in 2012. “Homeland security is going to be 24-7 for me. Maybe in a year or so things could change, but right now ­— and I’m not being cute ­— I really don’t expect it.”

It’s a similar story for Rep. Charlie Dent, the Pennsylvania Republican recently assigned to the Appropriations Committee, a position he has been actively seeking since before the 2008 elections.

“I basically developed a two-year strategy. I let people know I was interested,” he said in an interview. “Clearly, the real power of Congress is the power of the purse. Being on Appropriations puts me in the middle of that. … It’s one of the few places in Congress you can touch public policy in so many places.”

Dent says he’s been encouraged to challenge Sen. Bob Casey (D) in 2012 but suggested he’s content to hold on to his new committee assignment.

“One never rules anything out,” he said. But “at the same time I haven’t been actively pursuing it.”

Some Republicans warn it’s far too early to predict whether House shifts will shape the 2012 Senate electoral landscape, although it’s clear that every seat counts. Democrats hold 53 seats, including two Independents who caucus with them, compared with 47 seats for Republicans.

“I would concede that at first glance, early on, in a couple of states it might not be helpful,” one Republican campaign strategist said of the House committee promotions.

The strategist singled out Wisconsin as perhaps the most painful example, where some hoped that Rep. Paul Ryan (R) would challenge 75-year-old Sen. Herb Kohl (D), considered vulnerable amid speculation that he might not seek a fifth term in 2012.

But Ryan is the newly minted Budget chairman. And given House Republicans’ focus on spending cuts, it’s likely that he will be busy in the new Congress.

That has yet to quell local speculation that Ryan might challenge Kohl in a state where the GOP recently captured the governorship, both chambers of the Legislature, a Senate seat and two House seats.

All those factors, Wisconsin pols said, could make it attractive for Ryan to run statewide.

“The fact that today Republicans are taking control of the House has still not dissuaded talks” of Ryan running, Wisconsin-based consultant Scott Becher said.

Ryan turns 40 later this month and is widely considered a hot commodity on the national circuit. But now in his seventh term, he serves as the brain trust of the GOP conference.

He is often mentioned as a future presidential candidate, and as Becher pointed out, “How do you become president? You become a Senator or a governor.”

But the budget wonk has repeatedly said he is not looking to run for higher office anytime soon, whether it’s for a Senate seat, the governor’s office or the White House. GOP voters don’t appear to accept that message: Ryan received 52 percent of Wisconsin Republicans’ support for the Senate nomination in a Public Policy Polling survey conducted last month.

Ryan’s office did not respond to a request for comment.

In Ohio, Republicans said they believe they have an opportunity to knock off first-term Sen. Sherrod Brown (D), but it’s unlikely they’ll persuade Rep. Jim Jordan to accept the challenge.

The three-term incumbent was elected to lead the Republican Study Committee for the next two years, a leadership position that will give him an opportunity to lead what he calls the “conservative conscience on Capitol Hill.” Already, Jordan reports being inundated with speech requests for the coming months.

“I’m focused on the Republican Study Committee and my work here,” Jordan told Roll Call. But what about a Senate bid? He’s “leaning against that,” Jordan said, noting that he’s also excited about his new chairmanship of an Oversight and Government Reform subcommittee.

In California, Rep. Darrell Issa has been listed among Republicans interested in challenging Sen. Dianne Feinstein (D) in 2012. But the six-term Member is now chairman of the Oversight and Government Reform Committee and has assumed a much higher profile on Capitol Hill.

It is not a profile he is looking to change, spokesman Kurt Bardella said.

“Chairman Issa can do more to advance his agenda by staying here in the House and working at the Oversight and Government Reform Committee than he can by being one of 100 in the Senate,” Bardella said.

In 1998, Issa wanted to challenge Sen. Barbara Boxer (D) but lost the GOP primary despite spending nearly $10 million from his own pocket. Two years later he was elected to the House. He bankrolled the 2002 recall of then-Gov. Gray Davis (D), winning him plaudits among California Republicans, but the conservative has otherwise demurred from statewide politics.

Dave Gilliard, Issa’s California-based political consultant, said it will be tough to find a formidable candidate to challenge Feinstein next year.

“I don’t know anyone who is in the majority in the House who would want to give that up to take her on,” Gilliard said of Issa and other potential candidates, including Rep. John Campbell (R). “I think a lot of people would love to see [Issa] run in the future, but right now I think he’s focused on being in the majority and his committee chairmanship.”

Questions remain about Rep. Denny Rehberg, the Montana Republican largely thought to be weighing a run against first-term Sen. Jon Tester (D).

Rehberg has served on the Appropriations Committee since 2005, but he will play a more powerful role as part of the majority. It’s also unclear whether he might be awarded a chairmanship on one of the three Appropriations subcommittees. Such announcements are expected in the coming days.

“Denny is focused on doing the job the overwhelming majority of Montana voters sent him to Washington to do,” spokesman Jed Link said in response to questions about Rehberg’s Senate prospects in 2012.

Meanwhile, some committee promotions tell a very different story.

In at least one case, a House Republican might use his new status as a launching pad for a 2012 Senate bid. Rep. Connie Mack IV, the son of a former Florida Senator, will serve as the chairman of the Foreign Affairs Subcommittee on the Western Hemisphere, where he was previously the ranking member.

A Republican aide confirmed that the Florida Republican walked away from potential slots on the Ways and Means and the Energy and Commerce committees in favor of the subcommittee chairmanship. There were as many as three Florida slots available on Ways and Means, according to the aide, but such a position likely would not allow for the same visibility as the chairmanship, with which Mack plans to be “very active,” the aide said.

Specifically, Mack will devote considerable time to examining the national security threats posed by Venezuelan President Hugo Chávez, a high-profile issue in Florida. The Congressman is set to deliver a speech on the subject at next month’s national Conservative Political Action Conference.

Mack has also made a handful of key hires in recent months suggesting he’s gearing up for a Senate run. In addition to senior adviser David James, a veteran of three Republican Senate campaigns and the recent New York gubernatorial race, Mack is using general consultant Arthur Finkelstein, who worked on both of Mack’s father’s successful Senate bids.