Tea party groups and other prominent grass-roots conservative operations say they are on board with Stephen K. Bannon’s crusade to oust the entire slate of incumbent Republicans because the former White House political strategist is tapping into the same anti-establishment mood they have been sensing for a while.

The groups say they are active in every election but expect 2018 to be a banner year for ousting incumbent Republicans. They say their base is outraged that, despite having control of both the House and Senate, Republicans have yet to notch major conservative wins.

Mr. Bannon, who is now back running the right-wing Breitbart website, isn’t calling the shots for the movement, according to the groups. But the former Trump adviser is on to something.

“We’re going to be extraordinarily active,” said David Bozell, head of For America. “Some establishment guys, it’s not going to necessarily take a conservative movement upheaval to defeat them. You’re going to see a lot of folks stay home because of lack of results.”

Mr. Bannon left the White House this summer after the arrival of John F. Kelly as chief of staff. He returned to Breitbart.

He is also affiliated with Great America Political Action Committee, which in recent days has endorsed a Republican challenger to Sen. Jeff Flake, Arizona Republican. Mr. Flake announced Tuesday that he plans to retire rather than seek re-election — one week after Mr. Bannon endorsed his anticipated challenger, former state Sen. Kelli Ward.

Mr. Bannon also has endorsed an anti-establishment candidate in the Republican primary to take on Sen. Tammy Baldwin, Wisconsin Democrat, and has reportedly pledged to back a challenger to Sen. Dean Heller of Nevada, another vulnerable Republican incumbent.

Mr. Bannon also has met with a potential challenger to Sen. Roger F. Wicker, Mississippi Republican, and is searching for candidates in other races.

“It’s an open revolt, and it should be,” Mr. Bannon said at the rally in Arizona last week for Ms. Ward.

Senate Majority Leader Mitch McConnell, Kentucky Republican, said the right-wing challenges aren’t helpful to his job of stocking the Senate with Republicans.

“The goal here is to win elections in November. Back in 2010 and 2012, we nominated several candidates: Christine O’Donnell, Sharron Angle, Todd Akin, Richard Murdock,” Mr. McConnell said at the White House press conference. “They’re not in the Senate, and the reason for that was they were not able to appeal to a broader electorate in the general election.”

Indeed, former Alabama Chief Justice Roy Moore, whom Mr. Bannon backed over incumbent Sen. Luther Strange in that state’s special election, is tied in polling with the Democratic candidate in a deep-red state that should be an easy hold for Republicans. The general election for that race is set for December.

Some conservatives, though, said Mr. McConnell and other establishment Republicans have the system backward.

“Your job is to advance the conservative agenda that you promised the voter, and so that’s the goal. You’ll retain the majority by accomplishing the goal of advancing the conservative agenda that you promised,” Mr. Bozell said.

After the Alabama race, the next battle for the soul of the Republican Party in the Senate may be over fundraising.

Ken Cuccinelli, who heads the Senate Conservatives Fund, said party donors are wondering whether to pony up this cycle if it means bolstering incumbents who have failed to make headway on the conservative agenda.

“They’re insanely frustrated,” he said, adding that the energy ahead of next year’s elections is not with the party but with the outsiders challenging the establishment.

“The incumbents aren’t benefiting from activists. The challengers are,” he said.

John Feehery, a partner at EFB Advocacy and a Republican strategist, said while primary challengers can be good, the ones Mr. Bannon has chosen to back don’t appear much different from some of the fringe candidates in previous cycles.

“It’s a free country, and I don’t necessarily think that primary challenges are a bad thing,” Mr. Feehery said. “But Bannon has recruited some real winners who could end up making him and his movement very foolish.”

Other conservatives say that while the quality of the insurgent movement’s candidates varies from race to race, the real issue with Mr. Bannon’s cause is that it lacks an overall focus.

Ford O’Connell, a pro-Trump Republican strategist, said he doesn’t see Mr. Bannon’s efforts as benefits for the Trump agenda.

“His goal appears to be ousting McConnell more than pushing the Trump agenda,” he said.

Some of the senators Mr. Bannon promised to oppose voted with Mr. Trump a vast majority of the time, he said.

Mr. O’Connell agrees that incumbents need to be challenged but said Mr. Bannon must be more strategic about the races in which to become involved.

States like Nevada, where the Republican incumbent is especially weak, have been trending blue for the past few cycles now, and Mr. O’Connell said a fringe candidate could cost Republicans the seat.

“It’s not enough to challenge and defeat the sitting incumbent,” he said.

Out of 33 senators up for re-election next year, eight are Republicans. Of those, just one — Sen. Ted Cruz of Texas — is likely to have the right-wing groups’ backing.

“He’s really solidified his position, certainly on the Republican side,” Mr. Cuccinelli said. “We’re proud to support him, but we don’t often get in for incumbents.”

Mr. Cuccinelli said his group works on getting “new blood” in the Senate and typically looks to back candidates who don’t have major political platforms. He said the Senate Conservatives Fund decided to back Mr. Cruz this year mainly because of possible primary challengers from establishment Republicans.

“The establishment has been hunting around for primary challengers for him,” Mr. Cuccinelli said.

The last anti-establishment wave to crash over the Republican Party was in 2010, when a number of outsiders defeated party-backed candidates amid the emergence of a nationwide tea party movement.

Some of those tea party-styled candidates, such as Ms. O’Donnell in Delaware and Ms. Angle in Nevada, lost races that should have been easily winnable for the Republican Party.

Others, such as Sen. Marco Rubio of Florida, won and remain in Congress.

Jenny Beth Martin of Tea Party Patriots said anger among the tea party groups is elevated once again.

“They’re unhappy with [the] overall performance,” said Ms. Martin, pointing to a variety of issues where incumbents have failed, such as repealing Obamacare.

“They are looking for candidates that are going to champion our values more,” she said.

The conservative leaders bristle at the notion that Mr. Bannon is directing the push, though, saying the discontent among voters has been palpable and they have been channeling it for some time.

“I don’t think that Steve would want the mantle of being the leader of all this,” Mr. Bozell said. “I think that would make him cringe.”

“We’ve had conversations with people who are affiliated with Steve,” Ms. Martin said. “I’m friends with Steve, but I would say it’s just conversations we have with other conservative-leaning groups.”

The groups have also been slower than Mr. Bannon to pick favorites in some of the races where the former White House strategist has been meeting and recruiting candidates.

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