Passing legislation hasn’t been Rep. Jim Jordan’s strong suit, but that isn’t dampening the spirit of conservatives who are rallying behind his bid to become the 55th speaker of the House.

Instead, it is his ability to gum up the works, along with his near-unwavering support for President Trump, that is enchanting tea party and right-wing groups. They say they have been ill-served by a string of deal-making Republican leaders.

More than 100 conservative groups and top-level activists have announced their backing for Mr. Jordan in his bid to win the House’s top post if Republicans keep control of the House.

“He is firing the base up,” said Adam Brandon, president of FreedomWorks, which has vowed to invest a half-million dollars into Mr. Jordan’s speaker bid. “He has always voted like he campaigns, whether it has been on spending, Obamacare, his rhetoric matches up to his voting record, and few can say that.”

Mr. Jordan is widely considered a dark horse in the race to succeed Speaker Paul D. Ryan, Wisconsin Republican, who is not seeking re-election in November. Mr. Ryan and House Majority Whip Steve Scalise, Louisiana Republican, have thrown their support behind House Majority Leader Kevin McCarthy, California Republican.

But conservatives say Mr. McCarthy comes from the conciliatory wing of the party, and they are looking for a bruiser.

They insist Mr. Jordan has a chance to win because the House Republican conference could tilt further to the right after the November elections. They also say grassroots engagement on behalf of Mr. Jordan will put an unprecedented level of pressure on lawmakers to give him a good look.

“There is just so much disappointment with Republican leaders,” said Richard Viguerie, a veteran conservative leader. “The grassroots is starving for principled leadership, and they see that with Jim Jordan.”

Mr. Jordan, who co-founded the conservative House Freedom Caucus, has campaigned for the job in a series of radio and television interviews in which he praises Mr. Trump and argues that Congress has failed to back the president.

“We certainly helped with the tax cuts, and we shouldn’t downplay that. But where’s the border security wall we promised?” Mr. Jordan said on Radio America. “Where’s the Obamacare repeal? Where’s the welfare reform? Where’s defunding Planned Parenthood? Where are those key issues that we told the American people we were going to get done?

“We haven’t accomplished those, so if we keep the majority and I’m given the chance to lead the House, we’re going to focus on one simple message: doing what we told the American people we were going to do,” Mr. Jordan said.

The approach has won him praise from Mr. Trump, who invited Mr. Jordan on stage at a recent Ohio rally, sparking chants of “Speaker of the House.”

“What a great defender he’s been, what courage,” Mr. Trump said of Mr. Jordan. “I’ll tell you what. There is a brave, tough cookie along with some of his friends. … I didn’t know he was going to be here. I looked over and said, ‘I don’t want to wrestle him. He’s tough.’”

Mr. Jordan was a wrestler in college and later an assistant coach at Ohio State University, though that pedigree has come under fire in recent months. Some former wrestlers said he turned a blind eye to sexual misconduct.

Mr. Jordan has denied any knowledge of the misconduct. His allies call the timing of the accusations suspicious and say Mr. Jordan would never have recruited members of his own family had he been aware of such behavior.

Ken Cuccinelli, president of the Senate Conservatives Fund, said the discipline, commitment and determination that Mr. Jordan displayed throughout his wrestling career has served him well in the House and reinforced his image as a conservative warrior.

“He beat John Smith, the most decorated American wrestler in U.S. history,” said Mr. Cuccinelli, alluding to Mr. Jordan’s 1985 collegiate win over the eventual six-time World and Olympic champion. “He is one of the only people on the planet Earth to do this.”

Mr. Trump could use that kind of support at the head of the House, Mr. Cuccinelli said.

“Given the lack of support the president has gotten from the current leadership, you would think the Republican base, which has high favorable ratings of the president, would want the best fighter for the president as speaker,” he said.

Elected from Ohio’s 4th Congressional District in 2007 after serving a decade in the Ohio state legislature, Mr. Jordan became an early favorite of the tea party movement. In 2010, he was tapped as chairman of the conservative Republican Study Committee after the party flipped control of the House.

Mr. Jordan was a leading critic of Secretary of State Hillary Clinton’s handling of the 2012 attack in Benghazi, Libya, and has become known for his grilling of witnesses who testify before his congressional committees, including former CIA Director James B. Comey, former FBI agent Peter Strzok and Deputy Attorney General Rod Rosenstein.

“The guys that shine in those hearings, they endear themselves to the grassroots,” said David Bozell, president of ForAmerica. “There is a thirst for folks to take on the power structure in Washington, and Jim does that very, very well.”

Darrell West, vice president and director of governance studies at the Brookings Institution, said Mr. Jordan has endeared himself to conservatives by standing up for their principles and speaking his mind, even if that meant alienating others.

“He is consistent in his positions and does not back down from fights with powerful people,” Mr. West said. “He would be an unconventional choice for speaker because legislators generally want someone who can build majorities and not just score political points.”

Mr. Ryan and his predecessor, John A. Boehner, had those kinds of legislative pedigrees.

Mr. Boehner, also an Ohio Republican, ran the Education and Workforce Committee and was chief sponsor of the 2001 No Child Left Behind law, as well as other pension and education legislation.

Mr. Ryan wrote annual budgets as chief of the Budget Committee and then shepherded major free trade legislation through Congress as chairman of the Ways and Means panel.

Mr. McCarthy has served in leadership for years and has been instrumental in shepherding substantive pieces of legislation through the House.

In his 12 years in Congress, Mr. Jordan has never been the chief sponsor of a bill that has become law.

Perhaps his biggest moment came in 2013 when he and fellow members of the House Freedom Caucus led colleagues into a government shutdown, hoping they could use the annual spending process to force President Obama into negotiations over ending Obamacare. After 16 days of shutdown, Congress relented.

Mr. Boehner has not minced words in describing his fellow Ohioan, telling Politico last year that Mr. Jordan was a “legislative terrorist” who specialized in blowing up bills, not getting them passed.

Mr. Jordan’s backers, meanwhile, blame Republican leaders for bottling up conservative legislation and say Mr. Jordan’s willingness to shake up the status quo is exactly what his backers want.

“It is the heartbeat of the Jim Jordan excitement,” Mr. Bozell said.

Mr. Brandon said his group plans to promote Mr. Jordan’s bid through an ad campaign and a “Rally for the Republic” on Sept. 26 on the west lawn of the U.S. Capitol.

“FreedomWorks wants to flood the halls of Congress with the sound of your voice and make it perfectly clear to your members of Congress that you want conservative champion Jim Jordan as the next Speaker of the House and Judge Brett Kavanaugh on the Supreme Court,” the event invite reads.

Rep. Mark Meadow, chairman of the House Freedom Caucus, Rep. Dave Brat of Virginia and Sen. Rand Paul of Kentucky are scheduled to appear with Mr. Jordan.

Mr. Brat, also a member of the Freedom Caucus, said those backing Mr. Jordan aren’t worried about a thin record of legislative accomplishments.

“It is the most irrelevant question,” he said. “He has been at the lead with the Freedom Caucus on every issue … from Obamacare to the tax cut package to the budget and immigration. He is leading all of us right in the middle of it.”

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