WASHINGTON — One caller instructed Representative Adam Kinzinger of Illinois to slit his wrists and “rot in hell.” Another told Representative Don Bacon of Nebraska that they hoped he slipped and fell down a staircase. The office of Representative Nicole Malliotakis of New York has been inundated with angry messages tagging her as a “traitor.”

Investing in the nation’s roads and bridges was once considered one of the last realms of bipartisanship in Congress, and President Biden’s infrastructure bill drew ample support over the summer from Republicans in the Senate. But in the days since 13 House Republicans broke with their party leaders and voted for the $1 trillion legislation last week, they have been flooded by menacing messages from voters — and even some of their own colleagues — who regard their votes as a betrayal.

The vicious reaction to the passage of the bill, which was negotiated by a group of Republicans and Democrats determined to deliver on a bipartisan priority, reflects how deeply polarization has seeped into the political discourse within the Republican Party, making even the most uncontroversial legislation a potentially toxic vote.

The dynamic is a natural outgrowth of the slash-and-burn politics of former President Donald J. Trump, who savaged those in his party who backed the infrastructure bill as “RINOs” — Republicans in name only — who should be “ashamed of themselves.”

Mr. Trump’s frequent threats and insults directed at Republicans whom he considers insufficiently loyal have created powerful incentives for the party’s lawmakers to issue similarly bellicose statements. The former president’s approach has also encouraged an expectation among Republican base voters that their representatives will hew unswervingly to the party line.

Last week’s infrastructure vote has prompted intraparty warfare among Republicans, illustrating how just a few of the loudest voices in the party can — and will — direct a wall of ire at those who break with them even just occasionally.

“I regret that this good, bipartisan bill became a political football in recent weeks,” said Representative Fred Upton of Michigan, one of the 13 Republicans who backed the legislation. “Our country can’t afford this partisan dysfunction any longer.”

In the days following the vote, Mr. Upton’s phone lines were flooded with more than a thousand angry and threatening calls, including multiple death threats to him and his family, according to his office.

The visceral nature of the backlash is particularly striking because House Republican leaders who lobbied their rank-and-file to vote against the measure have made few substantive policy arguments against the plan, which will send hundreds of billions of dollars in federal money into states and congressional districts around the country for badly needed infrastructure improvements.

Some of them even conceded publicly that they would have backed such a bill had the political circumstances been different, complaining that Democrats had poisoned the well by pushing a separate $1.85 trillion social safety net, climate and tax plan at the same time.

Mr. Biden “should have focused just on infrastructure,” Representative Kevin McCarthy, Republican of California and the minority leader, said last month. “But what they want to do is restructure and transform America.”

“If they brought just an infrastructure bill by itself up, you would find, overwhelmingly, Republicans want to work with you and get one through,” he insisted.

But the Republicans who joined Democrats last week found themselves scapegoated almost immediately.

Hours after the 13 Republicans voted for the bill, explaining in statements that it would deliver badly needed money for transportation and other projects in their districts, Representative Marjorie Taylor Greene, Republican of Georgia, posted the phone numbers of their Washington offices on her social media accounts.

In separate posts naming them on major social media platforms — Ms. Greene has nearly half a million followers on both Instagram and Twitter — she branded them as “traitors.”

While Ms. Greene trained her ire on her colleagues, the social media channels of Stephen K. Bannon, Mr. Trump’s former chief strategist, blasted out the office phone numbers of the 19 Republican senators who voted for the infrastructure bill in August.

It appears their followers listened.

A vast majority of menacing phone calls to the offices of the 13 House Republicans have been made by voters outside the targeted lawmakers’ districts, according to several congressional aides who described the calls on the condition of anonymity because they were not authorized to comment publicly.

And while Ms. Malliotakis’s Washington office has received a litany of insulting, angry phone calls, a majority of callers to her Staten Island district office have been supportive of her vote, a spokeswoman said. (In an interview with CNN this week, Ms. Malliotakis credited Mr. Trump with laying the groundwork for passage of the bill, noting that the former president had often talked about the need for major public works legislation, but leaving unmentioned how he blew up several attempts to obtain a bipartisan deal on such a measure.)

Animating many of the irate calls, aides said, are various misunderstandings of what is in the infrastructure bill. In citing complaints about it, they say, an overwhelming majority of callers have taken issue with provisions contained in the separate social policy bill that Republicans have uniformly opposed — not the infrastructure bill.

Attempts by congressional aides to explain that the programs being criticized are not actually contained in the infrastructure bill have been shrugged off by the callers, whose main preoccupation appears to be their fury that any Republican had voted for a bill championed by Mr. Biden.

The exchanges have been particularly brutal for the young, low-level staff members who are tasked with processing constituent calls and have been called an array of unprintable epithets by angry callers, according to the aides. Such coarse, even violent language from callers has become more common for congressional offices in recent years, but it has been particularly jarring given the subject matter at hand: an infrastructure bill that will spread federal money around the country to repair aging roads, bridges and tunnels and expand high-speed internet access.

“To only get 13 votes from the House was very sad,” said Representative Peter A. DeFazio, Democrat of Oregon and the chairman of the Transportation and Infrastructure Committee, referring to Republican support for the bill. “But to have those people attacked for doing the right thing for the United States of America and everybody’s constituents?”

The anger could have damaging political consequences for House Republicans, whose ranks include both hard-right lawmakers who demand the total obstruction of Mr. Biden’s agenda and those who are willing to accept bipartisan deals to benefit their constituents.

Many of the Republicans who supported the infrastructure bill hail from crucial swing districts where voters tend to reward bipartisan pragmatism and efforts to reach across the aisle — districts that the party must hold if it wants to reclaim the House in next year’s midterm elections. Some of those lawmakers, like Mr. Upton and Representative John Katko of New York, have held onto their competitive seats in large part because of their reputations as sober-minded deal makers.

But there is little room for such figures in today’s Republican Party.

Representative Matt Gaetz of Florida argued on Tuesday that voting against the infrastructure bill was as important a conservative litmus test as voting against impeaching Mr. Trump, and he essentially dared party leaders to strip the 13 lawmakers of their seats on congressional committees as retaliation.

Mr. Trump, who groused privately on Monday night at a fund-raiser in Tampa, Fla., about the Republicans who voted for the bill, weighed in publicly on Tuesday, targeting Senator Mitch McConnell, Republican of Kentucky and the minority leader, for supporting the package.

“Why is it that old crow Mitch McConnell voted for a terrible Democrat socialist infrastructure plan, and induced others in his party to do likewise,” Mr. Trump asked in a statement, “when he was incapable of getting a great infrastructure plan wanting to be put forward by me and the Republican Party?”

Mr. Trump did not reference his own role in undercutting the effort to pass an infrastructure bill during his presidency when he torpedoed a meeting with Democratic congressional leaders in 2019, fuming that they could not investigate him and legislate with him at the same time.

On Tuesday, Mr. McConnell called the infrastructure bill a “godsend” for Kentucky at a news conference in his home state, according to a local television station.

“We have a lot of infrastructure needs,” Mr. McConnell said.

Emily Cochrane contributed reporting.