WASHINGTON — Senator Ted Cruz has led a government shutdown, takes pride in being despised in Washington, and until recently had zero supporters among his Senate colleagues. On the issues, he is unyielding: This week he called for security patrols in Muslim neighborhoods in the United States.

But now the Texas archconservative, once dismissed as a fringe player, has a prominent new role: the groom in a marriage of convenience with a desperate GOP establishment.

Heading into a crucial primary showdown in Wisconsin April 5, mainstream Republicans find themselves having to rally behind Cruz’s bid for the presidency as the only way to deny Donald Trump the party nomination.

At stake in this plot, rich with irony, is the future of the Republican Party.

“There’s that old saying that politics makes strange bedfellows. Well, this is probably the strangest of them all,’’ said Republican strategist Kevin Madden, who worked on the campaign of the 2012 nominee, former Massachusetts governor Mitt Romney, but is now unaligned.

Romney, who is leading a crusade against Trump, said he voted for Cruz in the Utah primary on Tuesday. Jeb Bush, whose own presidential campaign flamed out in South Carolina, endorsed Cruz this week. Senator Lindsey Graham, one of Cruz’s top critics who last month joked that no one would care if Cruz were murdered on the Senate floor, even hosted a fund-raiser for his onetime rival at a Washington saloon on Monday, raising more than $200,000.

This isn’t about any love for Cruz, which is in short supply among party leaders.

It’s about strengthening Cruz enough to stop Trump from securing the 1,237 delegates he needs to lock up the nomination. If he falls short, the goal would be to engineer the selection of a different candidate, in an exceedingly rare move, at the Republican National Convention in Cleveland in July.

“I think if it’s an open convention, it’s very likely it would be someone who’s not currently running,’’ Wisconsin Governor Scott Walker, who ended his own race for the White House last fall, told reporters on Thursday.

Walker has yet to make an endorsement but told Charlie Sykes, a Milwaukee talk radio host and political analyst, this week that Cruz was the only candidate left with a shot at stopping Trump.

Sykes endorsed Cruz this week via his conservative news forum, Right Wisconsin. He had previously supported Walker, then Senator Marco Rubio of Florida, who ended his bid last week after losing his home state. For Skyes and others Republicans, backing Cruz is a undesirable but necessary move.

“I am more anti-Trump than I am pro-Cruz,’’ Sykes said in an interview. “Right now Republican voters in Wisconsin are making the tactical decision that a vote for Cruz is number one, the only way to block Donald Trump, and number two, the only way to get to an open convention.’’

Polls show Cruz neck-and- neck with Trump in Wisconsin. Even by winning the state, Cruz still would face a virtually impossible task of amassing enough delegates to clinch the nomination. Cruz currently has 465 delegates, compared with Trump’s 739. Ohio Governor John Kasich has won only his home state and trails far behind with 143 delegates.

If Trump wins Wisconsin, it will be difficult to keep him from getting the majority of the delegates.

Wisconsin state Representative Jim Steineke, the Republican majority leader and a former Rubio supporter, also endorsed Cruz this week. He said he’ll likely campaign for Cruz throughout the state in the days leading up to the primary.

“If Senator Cruz is able to win Wisconsin, the nomination process would probably go to the convention, and at that point, all bets are off,’’ Steineke said. “I would be comfortable with Cruz as the nominee, but I wouldn’t necessarily discount the possibility of a different choice coming out of the convention.’’

Some GOP strategists say it is unlikely that the party would nominate a candidate other than Cruz or Trump — a move that would be seen as rejecting the will of the primary voters.

Cruz’s campaign has been diligently courting delegates and is securing signed pledges of loyalty to support him at the convention, said Rick Tyler, former Cruz spokesman.

The Club for Growth, a conservative group based in Washington that advocates for free-market principles, endorsed Cruz this week, the first time the organization has ever endorsed in a presidential race.

The group plans to raise money for Cruz’s campaign and will begin broadcasting a pro-Cruz television and digital ad in Wisconsin beginning Saturday. The $1 million buy features a 30-second spot highlighting delegate mathematics, emphasizing that only Cruz — not Kasich — could beat Trump.

None of this, of course, is positioning the party to compete in the general election.

As Cruz wages his come-from-behind effort, he and his allies find themselves dragged into a distracting battle over their wives. An anti-Trump super PAC fired the first shot by airing a Facebook ad targeting Utah Mormons that showed Trump’s wife, Melania, a former supermodel, posing nude. The ad introduced Mrs. Trump as the next First Lady — unless voters support Cruz. Trump retaliated by threatening to “spill the beans’’ on Cruz’s wife, Heidi, a Goldman Sachs executive.

On Thursday, Trump tweeted a side-by-side comparison of the two women that portrayed Mrs. Cruz in an unflattering light. An angry Cruz responded by calling Trump a “sniveling coward.’’

In the midst of that bizarre sideshow, Cruz, echoing harsh anti-Muslim rhetoric from Trump, generated attention this week after the Brussels bombings with a demand for a security crackdown in Muslim neighborhoods across America to root out radicalism.

Former secretary of state Hillary Clinton, the Democratic front-runner, called Cruz’s plans to patrol Muslim neighborhoods “wrong, counterproductive, and dangerous,’’ lumping Cruz with Trump in their calls for treating American Muslims like criminals.

Trump is advocating a ban on Muslims entering the country and wants to create a national registry of Muslims living in America.

Cruz kicked off his Wisconsin campaign Wednesday night with a live interview with Sykes in front of an audience of 350 voters, during which he defended his neighborhood patrol plans.

“We need to be using proactive law enforcement and intelligence and national security resources to prevent radicalism,’’ he said. “My focus is on stopping Islamists.’’

Tracy Jan can be reached at tracy.jan@globe.com. Follow her on Twitter @TracyJan.