The Wisconsin spring elections were less than a week away, and with the state’s coronavirus death toll mounting, Democrats were challenging Republican plans to hold the vote as scheduled.

In an emergency hearing, held via videoconference, John Devaney, a lawyer for the Democrats, proposed a simple compromise: Extend the deadline for mail ballots by six days past Election Day, to April 13, to ensure that more people could vote, and vote safely.

“That’s going to be much more enfranchising,” said Mr. Devaney, arguing one of the most politically freighted voting-rights cases since Bush v. Gore from his bedroom in South Carolina as his black lab, Gus, repeatedly interrupted at the door.

The presiding federal judge, William M. Conley, agreed, pointing out that clerks were facing severe backlogs and delays as they struggled to meet surging demand for mail-in ballots.

Yet with hours to go before Election Day, the Supreme Court reversed that decision along strict ideological lines, a decision based in large part on the majority’s assertion that the Democrats had never asked for the very extension Mr. Devaney requested in court. It was the first major voting-rights decision led by the court’s conservative newest member, Justice Brett M. Kavanaugh, and it was in keeping with a broader Republican approach that puts more weight on protecting against potential fraud — vanishingly rare in American elections — than the right to vote, with limited regard for the added burdens of the pandemic.

When the state released its final vote tallies on Monday, it was clear that the decision — arrived at remotely, so the justices would not have to brave the Covid-19 conditions — had resulted in the disenfranchisement of thousands of voters, forced several thousand more to endanger their lives at polls and burdened already strained state health officials with a grim new task: tracking the extent to which in-person voting contributed to the virus’s spread in the state, a federal disaster area.

While exact numbers were still unclear, Ben Wikler, the chairman of the Democratic Party of Wisconsin, said “every legal option is on the table” to contend what he called “a near certainty that thousands of people were disenfranchised.”

Though Jill Karofsky, the candidate backed by Democrats, was declared the winner on Monday night, exact vote totals were not likely to be tallied until late Monday night or Tuesday morning.

Before Judge Conley’s decision, state officials had estimated that at least 27,500 absentee ballots would come in too late to be counted — nearly five times the vote margin that decided the statewide judicial elections last year. As of Monday morning, more than 11,000 voters who requested ballots were never even sent one, according to data from the Wisconsin Elections Commission, though figures were continuing to update.

The number of disenfranchised voters was potentially higher. As of Monday, 185,000 absentee ballots remained outstanding, and election officials were trying to determine what percentage of those might have been returned had Judge Conley’s deadline of April 13 held. In Milwaukee, official tallies showed that the percentage of unreturned ballots was double its usual rate.

There was also the indeterminate number of voters who were too afraid to appear at polling stations on Election Day, by which point it would have been too late to request absentee ballots.

And then there was the matter of how to handle ballots that had not been postmarked with an exact date.

That question went at the heart of a seemingly arcane matter that is sure to bedevil states in November: whether to count mail-in ballots based on when they arrive or when they are postmarked, which, if Wisconsin is to be a guide, is already threatening to become the “hanging chad” of the 2020 election.

“Absentee ballots are going to be much more prevalent, and clerks around the country are going to be slammed the same way as they were in Wisconsin,” said Mr. Devaney, the lawyer who represented the Democrats in Wisconsin. How states settle on using postmarks, he added, “is going to be really important in terms of not disenfranchising thousands and thousands across the country.”

Wisconsin elections officials have spent days since the April 7 vote trying to determine how to count batches of mail-in ballots that had no postmark or had postmarks that featured only the month — April — and not the day on which they were stamped.

Because Wisconsin uses a “received-by” deadline for mail-in ballots, it has no legal definition for what constitutes an appropriate postmark on a ballot. Yet in rendering its decision imposing a postmark requirement of April 7, the Supreme Court majority wrote that “absentee ballots now must be mailed and postmarked by Election Day, Tuesday, April 7, as state law would necessarily require,” an important imprecision if not an outright error.

“Because the court decided to go its own direction,“ said Ann Jacobs, a Democratic appointee to the Wisconsin Elections Commission, “it created this artificial construct of a postmark without saying what a postmark is.”

The lower court judge’s ruling had set April 13 as a “received-by” deadline, which would have averted such confusion. After a Republican appeal, the United States Court of Appeals for the Seventh Circuit, which includes Illinois, Indiana and Wisconsin, upheld the decision.

Justice Kavanaugh is the member of the Supreme Court responsible for overseeing the Seventh Circuit, and the Republican National Committee’s application was addressed to him. As is usual in important cases, he referred the application to the full court.

Civil rights activists have closely followed his involvement in voting rights issues since his nomination in 2018, worried that he would become a reliable fifth vote in support of laws that make voting harder, regardless of their effects on traditionally disenfranchised groups like African-American and Hispanic people.

Under Chief Justice John G. Roberts Jr., the court had already seemed particularly inclined to favor restrictive voting laws, given its decision effectively striking down the most powerful provision protecting minority voting rights that had been enshrined in the landmark Voting Rights Act of 1965.

The majority opinion on the Wisconsin election was unsigned, which is typical when the court rules on emergency applications. But there are good reasons to think that its principal author was Justice Kavanaugh.

When the Supreme Court rules on emergency applications, the majority almost never gives reasons like the one it included with the Wisconsin decision. Justice Kavanaugh has made efforts to illuminate what practitioners call the court’s “shadow docket.”

In March 2019, for instance, he was the only justice to give an explanation for the court’s decision to stay the execution of a Buddhist inmate in Texas. A month earlier, he was the only one of four dissenting justices in an abortion case to explain his thinking.

Regardless of its authorship, the Wisconsin decision repeatedly mentioned that Democrats did not specifically seek to delay the absentee ballot deadline until April 13 in “preliminary injunction motions,” even though Mr. Devaney specifically did so while arguing before Judge Conley. That hearing had taken place one day after Gov. Tony Evers, a Democrat, requested a federal disaster declaration for his state.

And the decision appeared to contradict the tenet it sought to uphold, that “lower federal courts should not ordinarily not alter the election rules on the eve of an election.”

The Supreme Court ruling, coming late on the literal eve of an election taking place under conditions that were far from ordinary, resulted in chaos and confusion throughout the state.

In Milwaukee, home to 10 percent of the state’s population, the city had sent out tens of thousands of ballots with explicit instructions that explained the new deadline of April 13. So voters who did not tune into the news last Monday night would have had no way of knowing the instructions on their ballots were no longer valid.

“You’re talking somewhere around 35,000 to 40,000 people in the city of Milwaukee getting instructions with their ballots that they have until the 13th to return their ballot,” said Neil Albrecht, the executive director of Milwaukee’s election commission.

On Friday, four days after the election made national headlines, voters were still coming to the four drop-off bins placed at libraries around the city, casting votes that were clearly now invalid.

In Green Bay, the city clerk, Kris Teske, said her office had been planning to work through Wednesday to clear the backlog of hundreds of requests for mail ballots, but the Supreme Court decision basically ended that task; the ballots stayed put.

Where much of the legal focus has moved to ballots received after Election Day, there were complications related to ballots received on Election Day itself. The Wisconsin Elections Commission had sent guidance recommending that voters in quarantine wait 24 hours before handing their ballots to witnesses for requisite signatures, to avoid the potential spread of the coronavirus.

The absentee ballot of Lisa Schnell, who was self-isolating with her sister and not at her apartment outside Milwaukee, was accidentally sent to her normal residence, where her daughter was still living.

Heeding the new deadline set by the lower court, Ms. Schnell asked her daughter to send the ballot to her sister’s house by regular mail. When the Supreme Court knocked down the extension, Ms. Schnell’s ballot was stuck in the mail. And she could not get to a polling station.

“If I had known if that was going to happen, I would have had her overnight it to me, or we could have met somewhere in the middle,” she said. “It’s completely crazy.”