Republican Ben Sasse comfortably won his party's nomination for U.S. Senate in Nebraska Tuesday, handing the national tea party groups that backed him a much-needed victory headed into the heart of a congressional primary season offering few opportunities for success.

Ben Sasse, left, former Alaska governor Sarah Palin, Texas Sen. Ted Cruz, Sharon Lee and Utah Sen. Mike Lee, stand together at an April 25 rally. (Job Vigil, The Telegraph/AP)

A week ahead of U.S. Senate nominating contests in Kentucky and Georgia, where tea party candidates have fizzled, and a U.S. House primary in Idaho where the tea party challenger may lose, national conservative groups were nervously eyeing Nebraska, where they deployed substantial resources to support Sasse.

"Ben Sasse’s victory in the Nebraska Senate Republican primary shows the strength of the conservative movement. All three candidates ran as conservatives -- as GOP candidates are doing everywhere -- but Nebraskans weren't fooled," said conservative activist L. Brent Bozell III.

Sasse's win was a boon to the parade of conservative groups and figures who rallied to his side. Sens. Ted Cruz (R-Tex.) and Mike Lee (R-Utah) campaigned for Sasse alongside former Alaska governor Sarah Palin. The anti-tax Club for Growth and the Senate Conservatives Fund each spent at least hundreds of thousands of dollars supporting Sasse, the president of Midland University.

Sasse blunted a mini-surge from wealthy bank executive Sid Dinsdale, who appeared to emerge as a threat during the final week of the campaign amid a nasty advertising battle pitting Sasse and his allies against former state treasurer Shane Osborn, the candidate most closely aligned with the GOP establishment.

With all precincts reporting, Sasse defeated Dinsdale 49 percent to 22 percent, with Osborn running  third with 21 percent of the vote. Sasse will be a heavy favorite in the general election considering Nebraska’s strong conservative tilt.

GOP attention now shifts to next Tuesday, a day that has long been circled on Republican calendars because of the number of contested primaries being held. Tea party candidates face an uphill climb that day.

In Kentucky, Senate Minority Leader Mitch McConnell is the front-runner over conservative businessman Matt Bevin. Bevin's campaign has failed to gain much steam amid distracting setbacks like his attendance at a pro-cockfighting rally.

In Georgia, Rep. Jack Kingston, a powerful appropriator who has earned the ire of conservatives, appears to be near the head of a pack alongside businessman David Perdue in a Senate primary most close watcher believe is headed to a runoff. Tea party favorites like Rep. Paul Broun, meanwhile, are running well behind.

In Idaho's 2nd congressional district, the business wing of the GOP is battling the tea party in a fight that pits Rep. Mike Simpson against attorney Bryan Smith. Simpson is backed by the U.S. Chamber of Commerce. Smith is backed by the Club for Growth. ​

In some ways, Sasse is an unlikely bet to be championed by tea party groups that came to his defense. He previously spoke highly of the Medicare Part D prescription drug benefit, which the Club for Growth opposes. He told MSNBC he'd be comfortable supporting McConnell as the Senate GOP leader. The Senate Conservatives Fund backs Bevin's bid to unseat McConnell. Osborn attacked Sasse from the right on health-care during the race, airing ads accusing him of not opposing the federal health-care law forcefully enough.

An afterthought for much of the Nebraska campaign, Dinsdale, the president of Pinnacle Bancorp, Inc., loaned his campaign at least $1 million, which enabled him to hit the television airwaves hard during the stretch run of the race. Sasse's allies started ramping up their attacks against him during the final week.

The Club for Growth hit the airwaves with an attack ad casting Dinsdale as too liberal. Conservative blogger Erick Erickson, also a Sasse champion, wrote a piece highlighting Dinsdale's relatives' ties to groups that support abortion rights, an effort to weaken him in the eyes of conservative voters.

West Virginia also held its primaries Tuesday. In the Senate race, Rep. Shelley Moore Capito (R) and Secretary of State Natalie Tennant (D) advanced to a general election showdown as expected. Whoever wins the general election will make history as West Virginia’s first female senator. In the race for Capito's GOP-leaning district, tea party-backed candidate Alex Mooney won the GOP nomination and will face Democrat Nick Casey.