A showdown is taking shape in Congress over how far Washington should go in expanding voting access to respond to the coronavirus pandemic, with Democrats pressing to add new options for voters and President Trump and Republicans resisting changes they say could harm their election prospects in November.

Democrats are determined to add new voting requirements for November’s general election to the next stage of coronavirus relief legislation, a move that Mr. Trump and Republican leaders have vowed to oppose. But it is one that Democrats believe is necessary and all the more urgent in light of the confusion and court fights surrounding Wisconsin’s elections on Tuesday.

With public health officials encouraging social distancing and staying at home to slow the spread of the virus, the prospect of millions of voters congregating at polling places around the country to cast their ballots this fall appears increasingly untenable and dangerous. But the fight over whether the federal government should require states to offer other options — by allowing voting by mail, extending early voting and instituting other changes to protect voters and voting rights — is emerging as a major sticking point as lawmakers look to pass a fourth emergency aid measure in the next few weeks.

Democrats argue that changes are imperative, and Congress must make them now before it will be too late to put them in place for the November balloting.

“We can’t allow our democracy to go down the tubes because this administration did not prepare for this pandemic,” said Senator Amy Klobuchar of Minnesota, the top Democrat on the Senate Rules Committee, which oversees election law. “We have to come up with best practices and make sure that everyone can still vote.”

Mr. Trump, who in recent days has been ratcheting up his criticism of voting by mail, intensified his resistance on Wednesday, instructing Republicans in a tweet to “fight very hard when it comes to state wide mail-in voting” and saying it “doesn’t work out well for Republicans.” He also claimed there was “tremendous potential for voter fraud,” though there is little evidence to back up that assertion.

Elections experts say voter fraud in general is extremely rare, including fraud involving ballots mailed in by voters. Most mail-ballot fraud involves absentee ballots and is committed by corrupt campaigns or election officials, not voters — and even that is rare and generally easily caught. (Mr. Trump conceded on Tuesday that he voted by mail in Florida’s primary election in March.)

Still, the president made it clear last month that he regarded Democrats’ efforts to include broader voting access in the stimulus measure as a direct threat to Republicans’ electoral prospects. “They had things — levels of voting that, if you ever agreed to it, you’d never have a Republican elected in this country again,” Mr. Trump said then.

Voting by mail, which has been shown to increase turnout, is routine in many parts of the country and is the chief way of voting in states such as Colorado, Oregon and Washington. Yet some Republicans, taking their cues from Mr. Trump, have become increasingly open in making the argument that it is detrimental to their party’s political fortunes.

In an interview with a local call-in show, David Ralston, the Republican speaker of Georgia’s House, said a proposed vote-by-mail option for the state’s May primary would be a disaster for his party, explaining that the president had said it best.

“This will be extremely devastating to Republicans and conservatives in Georgia,” Mr. Ralston said. “This will certainly drive up turnout.”

Other Republicans say their opposition to Democrats’ proposals is driven by a belief that states should control their own elections and that, beyond providing sufficient money to conduct safe and fair voting, the federal government should stay out of their way.

“I’m philosophically opposed to the federal government taking over elections,” said Senator Roy Blunt of Missouri, the top Republican on the Rules Committee and a longtime state elections official himself. “It is a bad idea. I’m pretty flexible about the amount of money, but I’m not flexible about a federal takeover of the election process itself.”

Adding to the intensity over the fight is that Democrats and their allies see the forthcoming legislation as probably the last chance to force changes before it will be too late for states and counties to make adjustments in their election procedures for November. In a private conference call on Wednesday with House Democrats, Speaker Nancy Pelosi said she would push to include $2 billion for voting assistance in the next sweeping coronavirus crisis response package that is expected to be debated this month, according to people familiar with the conversation who described it on the condition of anonymity.

Democrats say they realize that it would not be feasible to initiate nationwide mail voting in this election cycle and they are simultaneously pressing for other, potentially less contentious new rules.

One measure with strong Democratic support calls for guaranteeing that all states allow at least 20 days of early, in-person voting to enable people to spread out their trips to polling places rather than lining up on Election Day. Introduced in March by Ms. Klobuchar and Senator Ron Wyden, Democrat of Oregon, it would also loosen existing restrictions in some states on who can cast absentee ballots; allow registration online and by mail at least 21 days before an election, or closer if states allow; and require all jurisdictions to develop a plan for voting in the event of an emergency.

“A big part of this will be voting at home,” Ms. Klobuchar said, “but it wouldn’t be only voting at home.”

Democrats fought to include their $2 billion request for significant changes in voting practices at the state level in the $2 trillion stimulus bill enacted last month. Republicans initially responded with an offer of $10 million, officials said, before the final amount was set at $400 million.

Democrats said they were disappointed with the absence of new voting accessibility requirements but did not want to hold up the emergency legislation over the election fight, since they assumed another bill would emerge and provide an avenue for enacting broad changes. Now, some lawmakers see a voting crisis emerging and promise that the coming fourth phase of government relief is their opportunity to do something about it.

“On the next bill, I intend to be far more determined and fierce on insisting on vote-by-mail,” said Senator Chris Coons of Delaware, the top Democrat on the Senate subcommittee that funds elections. “Mail voting is the method that best preserves the social distancing.”

Despite calls for Congress to institute new ballot and voting protections after foreign interference in the 2016 elections and voting disputes around the country, Republicans have been reluctant to do so, though they have supported an infusion of funds to help local elections officials make changes they see as necessary.

Senator Mitch McConnell, Republican of Kentucky and the majority leader, had drawn intense criticism for failing to act on proposals from the House. Republicans are likely to dig in on that position now that the president has taken such a strong stance against any changes. Republicans argue that Democrats are calling for the new voting rules only because they believe the modifications will give them an edge in the upcoming elections.

“Our Democratic friends want the federal government to take over elections, but historically those have been handled at the state level — I think that makes the most sense,” Senator John Cornyn, Republican of Texas, told reporters. “Actually that’s the safest, in terms of interference from outsiders. It’s actually our dispersed system that makes it harder for an adversary to come in and meddle with our elections. So, I don’t see that as being a part of this coronavirus response.”

Mr. Blunt said that local elections officials were best positioned to determine how to carry out their own elections and that federal interference would bog down decision-making. He said the federal government should provide the resources but leave the final say to local jurisdictions.

“If the states want to do all these things, I have no problem with it,” Mr. Blunt said. “This is a responsibility that the states have always had, and I think they would do it much better than the federal government. The federal government cannot do everything.”

But after the spectacle of thousands of Wisconsin voters risking potential exposure to the coronavirus while waiting in line to cast their ballots this week, and with elections around the nation being postponed, Democrats say it is time for the federal government to step in.

“When you look at what is happening in Wisconsin and what’s going on around the country, we can’t let this happen in the fall,” Ms. Klobuchar said.

She conceded that it was impossible to predict now what the state of the pandemic crisis would be in several months. “But whatever it is,” she said, “there is no reason that this early on we cannot reform our election process.”