Rep. Raul Labrador (R-Idaho) calls GOP lawmakers Monday seeking their vote by in Thursday's House Republican leadership elections. (Melina Mara/The Washington Post)

As he sat in his cramped, closet-size office Monday night, Rep. Raúl R. Labrador (R-Idaho) said he is running a long-shot campaign for House majority leader to not only make an ideological point, but to make a deeply personal one to his five children about the United States — that their father, a Mormon raised by a single mother in Puerto Rico, could contend for national power.

Taking a break from making calls to colleagues, Labrador picked up a booklet from his desk, his heavy eyes dampening as he read a handwritten letter from his oldest son, Michael. It described how he listened proudly to his father on Sean Hannity’s radio program last week as Labrador announced his bid.

“I’ve already won,” Labrador said softly as he put the booklet aside, tapping its cover.

But Labrador, a 46-year-old backbencher, is not expected to emerge victorious in Thursday’s House leadership election to replace Majority Leader Eric Cantor (R-Va.). House Majority Whip Kevin McCarthy (R-Calif.) is widely believed to have secured more than the 117 votes required to win — 51 percent of the 233-member House Republican conference.

Still, Labrador believes his candidacy is a necessary conduit for right-wing frustration with McCarthy’s otherwise uncontested rise in the wake of Cantor’s fall and that his is a courageous, if largely ad-hoc, effort.

Several conservative leaders, such as Matt Kibbe of FreedomWorks, have been rallying behind him, hoping that Labrador could become a cause for activists eager to see combative conservatives ascend. Labrador, who participated in the failed coup attempt against House Speaker John A. Boehner (R-Ohio) last year, is one of the sophomore hard-liners who have frequently quarreled with Boehner since 2010’s tea party wave.

When asked whether Sen. Ted Cruz (R-Tex.) urged him to run, Labrador would not confirm whether he had a conversation with the senator, smiling as he declined to comment.

With little time and little organization, Labrador has struggled to gain traction inside the GOP cloakroom — where relationships matter more than grass-roots fervor — finding few supporters outside of a tight-knit group of allies that includes Rep. Justin Amash (R-Mich.) and Rep. Thomas Massie (R-Ky.).

Labrador, however, believes that McCarthy is weaker than the confidence he projects, arguing that many members grouse privately about McCarthy’s vision and abilities — and that after Cantor’s loss, any candidate shouldn’t be written off.

“McCarthy’s support is pretty soft,” Labrador said. “Even the people who say they’re supporting him are not strongly supporting him. I have not had many people say they’re 100 percent excited about Kevin.”

“I hear he does know the names of spouses, which I guess is a big issue,” he added. “But you know, this shouldn’t be about personalities.”

Labrador said he was not planning to run until late last week when better known conservative members such as Rep. Jeb Hensarling (R-Texas) and Rep. Jim Jordan (R-Ohio) declined to challenge McCarthy, leaving the right flank without a contender for the second-ranking position in the House.

“That’s been the most difficult thing. We had an opportunity, but everybody here plays it so safe. They’re only willing to take a risk if victory is assured,” he said. “I spent three days trying to get Jim and Jeb to run.”

State politics distracted him, too. Over the weekend, he presided over Idaho’s state GOP convention and saw it fall into disarray amid infighting and procedural challenges.

Labrador’s clashes with McCarthy in recent years over the political direction of the House GOP is another factor in why he was willing to jump into a race that few Capitol Hill insiders think he has any chance of winning.

Months ago, Labrador said McCarthy took him out for dessert to try to soothe their differences, but their outlooks remain poles apart, especially over how McCarthy purportedly uses his position to “punish people” if they break away from the party line.

“That’s one of my gripes with the leadership in Congress, people are afraid,” he said. “They’re telling me, ‘Please don’t use my name or else I’ll get punished.’ ”

Earlier Monday, Labrador sent a letter to House Republicans outlining his pitch, writing, “Americans are looking for a change in the status quo.”

Labrador said he is also getting encouragement from House Republicans who would like to see more diversity in the leadership and that having him standing alongside Boehner would send a message to independent voters and minorities about the party’s future.

“Who better than a Hispanic former immigration lawyer to address the crisis at the border?” Labrador said.

But he acknowledged that he remains the underdog and that McCarthy’s extensive network and preparation for the leadership race will make it hard for him to make up ground in the final hours.

As Labrador made calls, McCarthy was in New York at a retreat for elected House leaders, his deputies shrugging off Labrador’s chances.

“I’m here trying to reach every Republican member,” Labrador said. “Remember, it’s a secret ballot and no one – no one — really knows how it’ll go.”