Nebraska state Senator Deb Fischer addresses supporters at the Republican Party headquarters Wednesday in Lincoln, Neb. (Nati Harnik/AP)

In Nebraska, one Republican Senate candidate, Jon Bruning, savaged President Obama’s health-care plan and compared welfare recipients to lazy, scavenging raccoons. He established himself as conservative enough to lock down the backing of the Tea Party Express.

But earlier this month, Bruning came under fire for being too liberal. “Big spender,” said the announcer in the TV ad. “Big taxer.”

Bruning’s best-funded opponent, Don Stenberg, had used his state office to support capital punishment and advance abortion limits. He had support of a conservative, free-market behemoth, the Club for Growth, but Stenberg, too, was criticized for being too loose with taxpayer funds.

On Tuesday, both men lost.

The winner of the Nebraska Senate primary was won by Deb Fischer, a state legislator who had managed to stay out of the red-on-red crossfire. She was known mainly for gaining the endorsement of conservative icon Sarah Palin, and for an ad where she compared her opponents to Angus cattle.

The Nebraska results were just the latest signal that the GOP might be drifting back into the nasty intra-party feud about conservative bona fides that dogged it in 2010.

This time, the clashes are more complicated, because the party’s rightward factions have splintered and separated, and each now wants to hold candidates to their own particular test of conservative purity. The insurgents are now under attack from new insurgencies.

The next fights will come in the Texas Senate race and in House races around the country. For the GOP, Nebraska was a reminder that its coalition includes powerful groups that want to shove the party rightward — and don’t mind losing an election, or an incumbent, to make their point.

“We’re not afraid of losing races. We think that there is, you know, some benefit to our involvement, win or lose,” said Chris Chocola, a former Indiana congressman who heads the Club for Growth. He meant that even when very conservative candidates lose, they scare incumbents into voting more conservatively.

“When the Republican party doesn’t act like Republicans, they get thrown out,” Chocola said. “I’m not sure that the current leadership has fully learned those lessons.”

In 2010, insurgent tea party groups helped defeat a number of establishment candidates in Republican primaries. Several of those upstart primary winners went on to victory in November’s general election, including now-senators Marco Rubio (Fla.), Mike Lee (Utah) and Rand Paul (Ky.).

But others fell flat. In Nevada and Delaware, particularly, weak and wacky Republican candidates lost, and let Democrats keep seats that had looked vulnerable.

This year, the same dynamic has already been repeated in Indiana, where longtime Sen. Richard Lugar (R) lost a primary to a more conservative, lesser-known challenger. Lugar was attacked for voting to confirm President Obama’s nominees for the Supreme Court and supporting economic bailout measures.

Now, polls show winner Richard Mourdock is a weaker general-election candidate than Lugar would have been. Still, Mourdock is running about even with his Democratic opponent, Rep. Joe Donnelly.

What happens now? In Texas, some insurgent conservatives are backing candidate Ted Cruz in a Senate primary against the better-known lieutenant governor, David Dewhurst. Outside groups are also trying to topple some incumbent Republicans in the House, including Energy and Commerce Chairman Fred Upton (R-Mich.).

“It was one thing to see Mourdock win. But when he won by 22 points, obviously that is very encouraging to me,” said Jack Hoogendyk, a state representative running against Upton with Club for Growth help. He said he would argue that Upton, who carries a 72.87 lifetime rating from the American Conservative Union, was too liberal. He has been criticized for voting to raise the debt limit, and supporting earmark spending in the past.

But Hoogendyk said that the mere fact that Upton had been in Washington for 25 years would also be a reason to doubt his conservative credentials. “Incumbency, it’s almost like a poison,”Hoogendyk said. “Anybody who is or is seen as establishment is at risk. It’s not just incumbents, but it’s people who represent incumbency or appear to be some sort of establishment candidate.”

The outcomes of these races might be less important than the battle to control what the word “Republican” means, and whether the Republican party itself gets a say in the matter. The nightmare scenario for GOP bosses is a party that continually turns on its elders, replacing them with newcomers who value notions of ideological purity over the party itself.

“There’s only been one perfect person ever walked the face of this Earth. And he ain’t gonna be our nominee this year, in any election,” Haley Barbour, a former Mississippi governor and Republican party chairman, said Wednesday.

“Unity is what it takes to win,” Barbour said. “And purity is the enemy of unity.”

In Nebraska, the GOP primary showed how thorough a modern purity test can be.

One attack on Bruning, for instance, said he has supported higher gas taxes and taxes on Social Security. That was a deviation in thought, not deed, and it was an old one. said the attack was based on a piece Bruning wrote in 1992, when he was a 23 year-old law student.

The Nebraska race also may have shown the risks of spending too much time on purity.

Fischer, the eventual winner, was considered by some to be the most moderate of the three candidates. She will now face the Democratic nominee, former governor and senator Bob Kerrey.

Staff writers Scott Clement and Tom Hamburger contributed to this report.