But Heller has spent the last few years working more closely with Democrats, aligning himself with Sen. Jack Reed of Rhode Island, for example, on unemployment insurance this year. The question for Heller will be whether he's prepared to do some damage to his burgeoning reputation as a centrist in the mold of Olympia Snowe to run what promises to be a nasty, national campaign for his party.
Asked about Heller's interest, spokesman Neal Patel emphasized the political work the Nevadan is already doing.
"Right now, Senator Heller's top priority is to help Republicans take over the Senate and make Mitch McConnell the majority leader," Patel said. "He knows personally how important it is to remain focused on the task at hand. To that end, Senator Heller has given nearly $400,000 to Republican candidates across the country this cycle and will continue working to help ensure they are elected."
Bob Corker, Tenn.
A one-time entrepreneur, with connections to the deep-pocketed business world, Corker was rumored to be in the hunt to chair the committee for the 2014 cycle. His name is circulating again among Republican political operatives ahead of 2016. In addition to his fundraising abilities, he is viewed as a strong recruiter, having deep ties to both the pro-Israel lobby, as the senior Republican on Foreign Relations, and to the financial world as a member of the Banking Committee.
But whether Corker, who relishes the art of compromise, wants the position is unclear. If the Republicans take the majority and he holds the Foreign Relations gavel, he may choose instead to focus on international affairs rather than the daunting domestic political challenge that will face Republicans in 2016.
"He has proven several times on national issues that he has strong ideas and understands what it takes to lead. I have no doubt he could bring that same insight and leadership to the NRSC and help the party going forward," said Hamilton County GOP chairman Tony Sanders.
Roger Wicker, Miss.
Wicker's chief selling point, say Republican strategists, is his connection to the politically influential Barbour family, which helped Sen. Thad Cochran defeat Chris McDaniel in Mississippi this cycle. Haley Barbour, then governor of Mississippi, appointed Wicker to the Senate after Trent Lott resigned. Wicker also supported Cochran in his tough primary fight, which was aided in large part by Haley's nephew, Henry Barbour. And those who know him also say he's a team player who regularly gives to the NRSC. "He's just doing everything he can to restore the Republican majority," said a Republican Senate aide.
But the fact that Wicker hails from Mississippi could also pose a problem: As one of the poorest states in the country, it does not provide a broad fundraising base.
A freshman Republican
Though this is a long shot, given the daunting map facing the party in 2016, some Republicans are suggesting that a first-term senator might be recruited to lead the committee. The thinking assumes that if Republicans win the majority in 2014, that 2016 will be so daunting that no experienced member would want to protect such a thin majority in a difficult year. Thom Tillis of North Carolina, for example, is in a tight race against Democratic incumbent Kay Hagan, but he has said already that he would like to chair the committee.