Republicans hit a significant stumbling block in their push to enact some of the strictest voting laws in the nation. But they could yet pass the measures through a special session of the Legislature.

Democrats in the Texas Legislature staged a dramatic, late-night walkout on Sunday night to force the failure of a sweeping Republican overhaul of state election laws. The move, which deprived the session of the minimum number of lawmakers required for a vote before a midnight deadline, was a stunning setback for state Republicans who had made a new voting law one of their top priorities.

The effort is not entirely dead, however. Gov. Greg Abbott, a Republican, indicated that he would call a special session of the Legislature, which could start as early as June 1, or Tuesday, to restart the process. The governor has said that he strongly supported an election bill, and in a statement he called the failure to reach one on Sunday “deeply disappointing.” He was widely expected to sign whatever measure Republicans passed.

“Election Integrity & Bail Reform were emergency items for this legislative session,” Mr. Abbott said on Twitter on Sunday night. “They will be added to the special session agenda.” He did not specify when the session would start.

While Republicans would still be favored to pass a bill in a special session, the unexpected turn of events on Sunday presents a new hurdle in their push to enact a far-reaching election law that would install some of the most rigid voting restrictions in the country, and cement the state as one of the hardest in which to cast a ballot.

The final bill, known as S.B. 7, included new restrictions on absentee voting; granted broad new autonomy and authority to partisan poll watchers; escalated punishments for mistakes or offenses by election officials; and banned both drive-through voting and 24-hour voting, which were used for the first time during the 2020 election in Harris County, home to Houston and a growing number of the state’s Democratic voters.

Republicans’ inability to pass the measure on Sunday night was the first major stumble for the party in its monthslong drive to restrict voting across the nation, and an embarrassment for G.O.P. leaders in the Texas Legislature who at least momentarily fell short of a top legislative goal for both the governor and the Republican Party.

After a lengthy debate in the State House of Representatives in which Democrats raised numerous objections, staged lengthy question-and-answer sessions and leveraged procedural maneuvers, Democrats left the chamber en masse, leaving the chamber roughly 14 members short of the required 100-member quorum to continue business. Without the requisite number of legislators, Dade Phelan, the speaker of the State House, adjourned the session around 11 p.m. local time, effectively killing the bill for this legislative session.

The Democratic flight was sparked by State Representative Chris Turner, the party’s caucus chair in the House, who sent a text message to members at 10:35 p.m. local time.

“Members, take your key and leave the chamber discreetly,” Mr. Turner wrote. “Do not go to the gallery. Leave the building. ~ Chris”

In a statement early Monday, Mr. Turner said the walkout had been a last resort.

“It became obvious Republicans were going to cut off debate to ram through their vote suppression legislation,” he said. “At that point, we had no choice but to take extraordinary measures to protect our constituents and their right to vote.”

Early Monday, Lt. Gov. Dan Patrick, a Republican, lashed out at his House colleagues and indirectly criticized the Republican leadership in the House, saying in a statement that it had “failed the people of Texas tonight. No excuse.”

If Mr. Abbott calls a special session, Republican legislators would have to start from scratch, but it is possible that they could simply use the same language and provisions from S.B. 7, or even introduce a bill with more strident restrictions on voting access.

From the outset, the push to install new restrictions on voting in Texas has been upended by legislative missteps and tension among Republicans in the State Capitol, marked by multiple late-night voting sessions in both chambers. After two different versions of the bill were passed by the House and the Senate, legislators took the bill behind closed doors to hash out a final version in a panel known as a conference committee.

State Representative Briscoe Cain, left, was one of the Republican sponsors of the voting legislation.
Jay Janner/Austin American-Statesman, via Associated Press

The conference committee took more than a week to finalize the measures, reaching an agreement on Friday, releasing the details of the legislation on Saturday and leaving both chambers with less than 48 hours to pass the bill.

A legislative power play by Republicans in the Senate late Saturday led to an all-night session and hours of impassioned debate and objections from Democrats. Early Sunday, the Senate passed the bill largely along party lines.

During debate late Sunday, State Representative Travis Clardy, a Republican, acknowledged that advancing the bill through the conference committee had proved to be a lengthy process, but he defended the panel’s methods.

“A lot of this was done late, I don’t get to control the clock,” Mr. Clardy said. “But I can assure you that the members of the committee did their absolute best, dead-level best, to make sure we’ve provided information to all members, including representative rows. And then we did everything that we could to make sure this was transparent.”

The effort in Texas, a major state with a booming population, represents the apex of the national Republican push to install tall new barriers to voting after President Donald J. Trump’s loss last year to Joseph R. Biden Jr., with expansive restrictions already becoming law in Iowa, Georgia and Florida in 2021. Fueled by Mr. Trump’s false claims of widespread fraud in the election, Republicans have passed the bills almost entirely along partisan lines, brushing off the protestations of Democrats, civil rights groups, voting rights groups, major corporations and faith leaders.

But the party’s setback in Texas is unlikely to calm Democratic pressure in Washington to pass new federal voting laws. President Biden and key Democrats in Congress are confronting rising calls from their party to do whatever is needed — including abolishing the Senate filibuster, which moderate senators have resisted — to push through a major voting rights and elections overhaul that would counteract the wave of Republican laws.

After the Texas bill became public on Saturday, Mr. Biden denounced it, along with similar measures in Georgia and Florida, as “an assault on democracy,” blasting the moves in a statement as “disproportionately targeting Black and Brown Americans.”

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He urged Congress to pass Democrats’ voting bills, the most ambitious of which, the For the People Act, would expand access to the ballot, reduce the role of money in politics, strengthen enforcement of existing election laws and limit gerrymandering. Another measure, the narrower John Lewis Voting Rights Act, would restore crucial parts of the 1965 Voting Rights Act that were struck down by the Supreme Court in 2013, including the requirement that some states receive federal approval before changing their election laws.

Aside from Texas, multiple states, including Arizona, Ohio and Michigan, have legislatures that are still in session and that may move forward on new voting laws. Republicans in Michigan have pledged to work around a likely veto from Gov. Gretchen Whitmer, a Democrat, by collecting signatures from citizens and seeking to pass new restrictions through a ballot initiative.

Nitashia Johnson for The New York Times

Republican lawmakers in battleground states have been backed in their effort by a party base and conservative media that have largely embraced the election falsehoods spread by Mr. Trump and his allies. G.O.P. legislators have argued that the nation must improve its “election security” even though the results of the last election have been confirmed by multiple audits, lawsuits, court decisions, election officials and even Mr. Trump’s own attorney general as free, safe, fair and secure.

In debate late Sunday night, Democratic legislators seized on a provision added late in the process that would make it easier to overturn the results of an election in the state in some circumstances. Texas law previously required proof that illicit votes had resulted in a wrongful victory. The new measure says that the number of fraudulent votes would simply need to be equal to the winning vote differential; it would not matter for whom those votes had been cast.

“They can use this to overthrow the voice of the people, to overthrow the voice of Texas,” said State Representative John Bucy III, a Democrat from near Austin. “Do we want to throw out our ability to let the voices be heard through elections?”

As with bills passed in other states, voting rights groups said the new provisions in Texas, if passed, would be likely to disproportionately affect poorer people and those of color.

“All the provisions have an impact on minorities one way or another,” Gilberto Hinojosa, the chair of the Texas Democratic Party, said on Sunday. “That’s what it’s intended to. They’re not trying to stop Republicans from going out to vote. They’re trying to stop Democrats from going out to vote and the base of the Democratic Party is overwhelmingly African-American and Hispanic.”

Republicans in the Legislature had defended the bill, falsely arguing that it contained no restrictions on voting and saying that it was part of a yearslong effort to strengthen election security in the state. Even so, they acknowledged that there was no widespread voting fraud last year in Texas, and the Republican secretary of state testified that the state’s election was “smooth and secure.”

“This isn’t about who won or who lost, it’s really to make the process better,” State Senator Bryan Hughes, one of the Republican sponsors of the bill, said in an interview this month. “We want to make the elections more accessible and more secure, make them smoother.”

Briscoe Cain, the sponsor of the bill in the House, said late Sunday that the bill was meant to ensure that “conduct of elections be uniform and consistent throughout the state, to reduce the likelihood of fraud and the conduct of elections, to protect the secrecy the ballot, promote voter access and ensure that all legally cast ballots are counted.”

Voting rights groups have long pointed to Texas as one of the hardest states in the country for voters to cast ballots. One recent study by Northern Illinois University ranked Texas last in an index measuring the difficulty of voting. The report cited a host of factors, including a drastic reduction of polling stations in some parts of the state and strict voter identification laws.

David Montgomery contributed reporting from Austin, Texas. Reporting was also contributed by Austin Ramzy and Anna Schaverien.