Sen. John Cornyn (Texas) is signaling an interest in taking on a rare second term as chairman of the National Republican Senatorial Committee next cycle, and his colleagues are privately encouraging him to do so as the party eyes pickups this fall and the possibility of reclaiming the majority in 2012.

If Cornyn were to lead the NRSC for another cycle, he would be following in the footsteps of another repeat chairman, Minority Leader Mitch McConnell (Ky.), who led the campaign committee during the 1998 and 2000 cycles. The job is viewed as a steppingstone to higher leadership posts, and Cornyn, a rising conservative star, is often mentioned as a possible future leader of the Conference.

Republican operatives on and off Capitol Hill give Cornyn high marks for the NRSC’s fundraising, candidate recruitment and messaging efforts. GOP Senators are almost universally pleased with Cornyn’s approach to running the campaign arm, and senior Republican aides say he has received an unprecedented level of assistance from a Conference notorious for ignoring its campaign committee.

Cornyn aides downplay their boss’s interest in leading the NRSC beyond this year’s midterm elections, saying he remains focused on gaining GOP Senate seats and that much can happen between now and Nov. 2. But Sen. Orrin Hatch (Utah), Cornyn’s deputy at the committee, predicted Republicans would ask the Texan to take on a second tour — and on Wednesday the NRSC chairman signaled his openness to doing so.

“I’m going to finish the job that I’ve signed on to do between now and November. I mean, I hope the outcome is such that people will be pleased. But it’s still too early to say. This takes a lot of time and effort; I’m not sure I want to do it again,” Cornyn said in a brief interview. “But I’m a team player, and I’m willing to listen.”

Who succeeds Democratic Senatorial Campaign Committee Chairman Bob Menendez (N.J.) seems far less certain. Menendez is unlikely to be a candidate for the post in the 2012 cycle because he will be up for re-election — usually a disqualifier for the demanding and time-consuming job. Freshman Sen. Mark Warner (D-Va.), a multimillionaire businessman, former governor and onetime state party chairman, appears to be the leading contender, according to Democratic sources and lobbyists who keep tabs on the DSCC.

Asked about his interest in the job on Wednesday, Warner played coy. “I don’t even really like raising money,” although he added with a chuckle: “I’m anxious to support leadership.”

[IMGCAP(1)]Under then-DSCC Chairman Charles Schumer’s (N.Y.) leadership during the 2006 and 2008 cycles, Senate Democrats picked up a total of 14 seats, and in 2006 Schumer helped the party win back the majority. The Democrats had the political wind at their back, although that wasn’t yet the case when Schumer took over in late 2004. The New Yorker was credited with running a top-flight operation that excelled on all fronts — particularly fundraising — and helped his party fully maximize its Senate opportunities.

The 2010 elections are still six and a half months away, but Cornyn is already receiving similar praise. Republicans say they are particularly impressed given the fact that Cornyn assumed the NRSC chairmanship on the heels of the biggest Democratic gains in a generation and during a historical low point for the GOP. In fact, several political observers had initially predicted further Senate losses for Republicans in 2010.

“I think Cornyn is as good as anybody I’ve ever seen in that position,” said Hatch, now serving in his sixth Senate term. “I think everybody in our Conference is pleased that we have somebody that energetic and outgoing and effective working for us. I have no doubt he’ll be asked to do it again. You’re never going to get a better one, I don’t think.”

K Street and Republican political consultants seem equally pleased, arguing that Cornyn wisely acknowledged early on that his brand of conservatism couldn’t win everywhere and showed a commitment to recruiting viable Republican candidates who could win. Republicans say Cornyn showed success throughout 2009 in recruiting candidates even when the party was still facing strong headwinds.

“He’s got great political sensibilities,” said one Republican operative based downtown.

Even as Cornyn was running for re-election in 2008, the ambitious Texan began transferring campaign funds to the NRSC and moving quietly to relinquish his Conference vice chairmanship and take the helm of the campaign arm.

Sen. John Ensign (Nev.), then the NRSC chairman, wasn’t interested in serving a second term, and then-Sen. Norm Coleman (Minn.), who did want the job, was unable to challenge Cornyn because his re-election contest with now-Sen. Al Franken (D) ended up in a protracted recount. Franken was finally declared the winner in June.

If any factor is working against a second term for Cornyn, it’s the demands of the job and the fact that he’ll have spent three and a half years campaigning for himself, GOP Senate candidates or incumbents. A second term chairing the NRSC would take him directly into his re-election race in 2014. But with likely GOP pickups this cycle and a Senate map that favors Republicans again in 2012, another go-around at the committee has its appeal.

Cornyn recognizes that any hope he has of influencing policy rests with winning enough seats to take back the majority, if not win the crucial legislative votes that Republicans have been losing consistently. Cornyn credited Sen. Scott Brown’s (R) January special election victory in Massachusetts with opening the GOP recruiting floodgates. Cornyn also credits his colleagues and his staff at the NRSC for the plaudits he has received.

“One thing I’ve found: You have to get elected before you make policy. I’ve run in 14 contested elections myself, and I enjoy that — to a point. But in most ways I’ve always considered it a necessary evil to do what I really wanted to do, which is to make policy,” Cornyn said. “But I found ourselves after 2008 in such diminished numbers that we really weren’t in a position really to influence policy. So, this is a necessary part of getting our numbers back to where we can. As Sen. McConnell likes to say, ‘If we get enough Republicans elected in November, we can help make this president a moderate.'”

Shira Toeplitz contributed to this report.