In the fight over Representative Jim Jordan’s bid for speaker, moderate Republicans are racing to outrun the chaos their party unleashed.If there is one thing Representative Mike Lawler of New York wants his constituents to know these days, it is that his political party is an absolute mess.“Stuck on stupid,” he branded a band of hard-right Republicans who pulled Congress to the brink of a government shutdown. He said their ouster of Speaker Kevin McCarthy “undermined the will of the American people.” As for the fight over a replacement that has ground the House to a halt for two weeks and counting?“This is the single stupidest thing I’ve ever seen politically, in terms of self-sabotage,” Mr. Lawler said in a telephone interview on Wednesday, just minutes after he joined 21 other Republicans and every Democrat to torpedo Representative Jim Jordan, a hard-right Ohioan, the latest candidate for speaker.His mounting frustration, voiced in interviews with reporters in the Capitol and on networks like CNN that are typically reviled on the right, is not merely an unusual display of bluntness. It is a risky gambit by one of the House’s most endangered Republicans to insulate himself from his own party as it careens, leaderless, toward another possible shutdown.Mr. Lawler’s outspokenness is perhaps the most glaring example of the balancing acts that anxious frontline Republicans are trying to pull off across the country — acrobatics that could determine the trajectory of the House this fall and beyond.The stakes are especially clear in New York, where Mr. Lawler and five fellow Republicans almost single-handedly helped deliver their party’s narrow House majority by flipping suburban districts from Long Island to the Hudson Valley.In almost every case, they won on hostile turf last year by assembling fragile coalitions comprising traditional conservatives and centrist Democrats attracted by the promise of a moderate counterbalance in Washington. Now, a push started by a small band of far-right agitators and a potential Jordan speakership threaten to shred those bonds and jeopardize Republicans’ standing with crucial swing voters ahead of 2024.Representatives Nick LaLota, left, and Anthony D’Esposito, who both represent Long Island districts won by President Biden, joined Mr. Lawler in voting against Mr. Jordan.Kenny Holston/The New York TimesNow, as they face intense pressure from their left and right flanks, a group of New York moderate Republicans that has mostly navigated key decisions as a bloc has increasingly begun to splinter, with four bucking their party and voting against Mr. Jordan.Representatives Anthony D’Esposito and Nick LaLota, who both represent Long Island districts won by President Biden, joined Mr. Lawler in voting against Mr. Jordan and have condemned those who took out Mr. McCarthy. So did Andrew Garbarino, another Long Islander who represents a district that Mr. Biden lost narrowly.All three voted for Lee Zeldin, their former colleague and onetime Republican candidate for governor in New York, even though Mr. Zeldin is no longer in office. They also issued near-identical statements outlining bipartisan priorities that they believed would falter under Mr. Jordan, the leader of the party’s rebellious right wing who has long been labeled a “legislative terrorist.”“I want a speaker who understands Long Island’s unique needs,” said Mr. D’Esposito, who represents a district where voters favored Mr. Biden by 14 points in 2020. He listed support for victims of the Sept. 11 terrorist attack and lifting a cap on the amount of state and local taxes that can be deducted on taxpayers’ federal return.But Representative Marc Molinaro, a moderate who narrowly flipped a Biden district in the Hudson Valley on promises of bipartisanship, appeared to have reached a very different conclusion: that the damage of elongating the House’s paralysis would be worse than electing a right-wing speaker whose policies and style could scarcely be more different than his.“Most of people I represent wouldn’t know the speaker of the House if they backed over them with a pickup truck,” he said before voting for Mr. Jordan.Representative Brandon Williams, a Republican from the Syracuse area who voted for Mr. Jordan, has evidently chosen not to give voice to the issue at all.As for Representative George Santos’s concerns, they appear to be far more personal. Under federal indictment on 23 counts and with virtually no path to re-election, he is facing a push by his fellow New York Republicans to expel him from Congress. Whoever emerges as the next speaker will be likely to determine how quickly such a vote takes place.“We need to rally behind one man, and that man has largely now been identified as Jim Jordan,” he said on Monday in a video posted to X, the platform formerly known as Twitter.Republican lawmakers caution that there is still time to put the House back in order, and moderates appeared to be coalescing late Wednesday around trying to empower a respected House veteran, Patrick T. McHenry, to serve as a temporary speaker until Congress can reach a deal to fund the government and address the war breaking out in Israel and Gaza.Some moderates want Representative Patrick McHenry to serve as temporary speaker.Anna Rose Layden for The New York TimesBut many fear damage is already being done. Democrats have deployed aggressive tactics to try to lock in the dysfunction with potential voters, as they eye the handful of seats they need to retake the House next year.The House Majority PAC, House Democrats’ primary super PAC, placed thousands of robocalls in Mr. Lawler’s district on Monday asking voters to pressure him not to support Mr. Jordan for speaker, given Mr. Jordan’s vote to overturn the 2020 election and “an extreme agenda to ban abortion nationwide.”Mr. Lawler did not vote for Mr. Jordan; Democrats hit him anyway. “Mike Lawler is an unserious legislator whose wasted vote today is blocking critical work getting done on behalf of Lower Hudson Valley families,” Ellie Dougherty, a spokeswoman for the Democratic Congressional Campaign Committee, said in an email blast.She issued similar quotes about Mr. D’Esposito and Mr. LaLota, while writing in another that Mr. Molinaro’s vote proved that he “embraces the far-right wing of his party.”At the same time, though, Republicans pushing too hard against their own party run the risk of sharp backlash from a right flank enamored of Mr. Jordan and eager to jump-start the House’s presidential impeachment inquiry and to fund new weapons for Israel’s battle against Hamas. In Mr. Lawler’s case, they played a key role in helping him topple Sean Patrick Maloney, the chairman of the Democratic campaign committee at the time, in one of the nation’s biggest upsets.Jack Chatham, a conservative talk radio host based in Albany, said on air on Tuesday that Mr. Lawler was “tempting fate,” particularly given the large number of retired law enforcement officers in his district, by opposing Mr. Jordan.Mr. Lawler, 37, said he could not get behind Mr. Jordan’s brand of politics and believed House Republicans — including their speaker candidate — had yet to reach a consensus that would allow them to govern.“So far this year, you have a group of people who have sought to undermine the majority, vote against the rules, vote against the speaker, move to vacate the speaker,” Mr. Lawler said. “That has been a challenge, and it hasn’t really been addressed.”He insisted Democrats, who refused to rescue Mr. McCarthy, should also share some blame politically. “Obviously, the longer this drags on, the worse it is,” added Mr. Lawler, a former political operative.For now, though, there are signs voters are cutting him some slack. Al Samuels, the head of the nonpartisan chamber of commerce in Rockland County, said Mr. Lawler needs to “protect how he is viewed” amid a national “embarrassment.”“I’m an old guy,” he said. “I believe in centrism and I believe we’re at our best as a nation when we reject the extremes, either right or left.” More