Nebraska Gov. Dave Heineman’s (R) second look at challenging Sen. Ben Nelson (D) creates a promising opportunity for Senate Republicans — but it could also wreak havoc on the GOP primary in a race that tops the party’s list of targets.

Sen. Jim DeMint (S.C.), an influential player among conservatives, said he was displeased after hearing Senate Minority Leader Mitch McConnell (Ky.) and National Republican Senatorial Committee Chairman John Cornyn (Texas) have been pressing the popular governor to reconsider his earlier decision not to run.

“Obviously I’m just disappointed that the party folks in Washington think they need to recruit someone else,” DeMint, who supports another GOP candidate in the race, said in an interview Tuesday. “Nebraska is a race the Republicans should win. … There are some good candidates in that race already.”

Republicans need a net gain of four seats next year to take outright control of the Senate, and it’s hard to conceive of a path to the majority that doesn’t run through Omaha. Public polls show Nelson remains one of the most vulnerable Democrats up for re-election next year.

So far, none of the three GOP challengers in the race have proved to be Nelson’s perfect foil — stoking fears that the Nebraska Senate race could escape the GOP’s grasp. Over the past several months, state Treasurer Don Stenberg, DeMint’s endorsed candidate, struggled with fundraising, Attorney General Jon Bruning has confronted ethical issues, and state Sen. Deb Fischer failed to raise the kind of money needed to boost her name identification.

Heineman initially ruled out a bid last year, but more recently he hinted to local reporters that he might be open to the race following repeated pleas from party leaders in Washington, D.C.

“They initiated the phone calls, and I listened to them,” Heineman said Tuesday morning, according to the Omaha World-Herald. “I also indicated that it would take a lot to change my mind.”

Senate leaders are mum about a potential Heineman candidacy. A visibly uncomfortable Cornyn balked Monday night at the Capitol when questioned about whether Heineman is reconsidering.

“I don’t have anything to add to what he said,” Cornyn told Roll Call. When asked whether his overtures to Heineman sends a message to the other GOP candidates that they are lacking, Cornyn replied, “I talk to every single one of them.”

DeMint said he has already given his opinion to Cornyn.

“I’ve already talked to John about it and let him know that grass roots around the country are concerned that party folks up here” are trying to meddle in the Nebraska primary, DeMint said. “We have a good relationship, but we disagree on this particular race. But it’s just going to make me work that much harder.”

Many national Republicans believe Heineman could clear the primary — and possibly the general election, too. Nelson has not said yet whether he’ll seek re-election, pushing off a final decision to the end of the year.

Democrats hope he’ll stay in the race and have already spent more than $1 million this cycle to boost his candidacy.

“He is going to be deciding here in the next few weeks whether he is going to run or not,” Democratic Senatorial Campaign Committee Chairwoman Patty Murray (Wash.) told reporters at a Tuesday briefing. “I want Ben Nelson to run. I think he absolutely is the best candidate,” she said later.

National Republicans believe a Heineman candidacy would have a “game over” effect on the Senate race. But local Republicans say there’s no way Bruning or Stenberg would step aside for the governor.

There’s no love lost between Heineman and Bruning, the current frontrunner for the GOP nomination. Republicans described a simmering tension between the two Republicans in their current elected capacities.

What’s more, Bruning backed former Rep. Tom Osborne’s primary challenge to Heineman in 2006. The attorney general also had $1.6 million in the bank at the end of September to spend on his bid. Stenberg won’t budge either, especially with DeMint’s backing. A meager fundraiser, Stenberg had just $18,000 in the bank at the end of September. DeMint said he’s helped him raise at least $100,000 for his campaign since then through his Senate Conservatives Fund.

While Heineman would be favored in the primary, there’s no way he emerges victorious in a better position than he started the race. And given the governor’s outspoken love for his current job, some local Republicans questioned how serious the former Capitol Hill aide is about running. They surmised he might be teasing his longtime adversary, Nelson, to get him out of the race.

“I think it’s clear from what Gov. Heineman has said that he enjoys being governor, and this is what he really likes to do,” said Phil Young, a former Nebraska Republican Party chairman. “But Gov. Heineman is also a team player, and the question will become how important he feels it is for him to be a candidate to make that a Republican Senate seat.”

If Heineman gets into the race, Senate Republicans might witness one of their ugliest intraparty battles of the cycle.

McConnell and Stenberg have history dating back to Nelson’s first Senate bid in 2000. Stenberg came within 2 points of defeating Nelson, despite being outspent by $1 million. Stenberg was never favored to win that race, which tightened in the final weeks.

There’s still grumbling in Nebraska GOP circles about whether it was Stenberg’s lackluster campaign or the NRSC’s last-minute messaging that caused Republicans to come up short.

It was McConnell who was calling the shots at the NRSC as chairman that cycle.

Abby Livingston contributed to this report.