A coronavirus outbreak that infected President Donald Trump and spread to the Senate threw a fresh element of uncertainty Friday into the politically fraught fight over installing Judge Amy Coney Barrett on the Supreme Court before Election Day, as Republicans vowed to press ahead and Democrats insisted on a pause.

Pulling off a complex confirmation that touches all three branches of government in the four weeks remaining before the election always promised to be a daunting task for Republicans in the middle of a pandemic. But by Friday evening, with the White House and Congress in turmoil and two Republican members of the Judiciary Committee, Sens. Mike Lee of Utah and Thom Tillis of North Carolina, among those announcing they had tested positive for the virus, it was clear that the challenge had grown steeper.

Top Republicans insisted they would move ahead at an uncommonly swift pace to hold hearings on Barrett’s nomination by Oct. 12, send her nomination to the full Senate by Oct. 22 and confirm her as soon as Oct. 26, eight days before Election Day — even if it meant breaking Senate norms and considering a lifetime judicial nomination by videoconference. But the latest outbreak raised the possibility that Republicans could lose their slim majority in the Judiciary Committee or on the Senate floor.

It gave Democrats, who were already objecting to Trump’s push to install a new Supreme Court justice so close to the election, a new reason to call for a delay. Seeing a potential opening, top Democrats called for the Senate to pause and assess the scope of the outbreak. They declared that a fully virtual hearing for a candidate for a lifetime appointment to the nation’s highest court would be unacceptable.

“It’s critical that Chairman Graham put the health of senators, the nominee and staff first — and ensure a full and fair hearing that is not rushed, not truncated and not virtual,” Sens. Chuck Schumer of New York, the minority leader, and Dianne Feinstein of California, the top Democrat on the Judiciary Committee, said in a joint statement. “Otherwise, this already illegitimate process will become a dangerous one.”

On Friday evening, after Tillis announced his positive test result, Schumer renewed his call for delay, writing on Twitter that going forward with hearings would be “irresponsible and dangerous.”

“There is absolutely no good reason to do so,” he said.

But Sen. Lindsey Graham, R-S.C., chair of the panel, vowed he would stick to his schedule, and Sen. Mitch McConnell, R-Ky., the majority leader, said he intended to move the nomination as soon as the committee approved it.

“Just finished a great phone call with @POTUS,” McConnell wrote on Twitter on Friday. “He’s in good spirits and we talked business — especially how impressed Senators are with the qualifications of Judge Barrett. Full steam ahead with the fair, thorough, timely process that the nominee, the Court, & the country deserve.”

Republican officials said they had no doubt that senators would find a way to muscle through the nomination over Democrats’ protests. But Republicans cannot afford to have many members sidelined by illness, which could provide Democrats an opportunity to stall the proceedings. Two Republican senators, Susan Collins of Maine and Lisa Murkowski of Alaska, have already raised objections to moving ahead before the election, reducing the wiggle room in the 53-47 Republican majority.

McConnell has insisted throughout the pandemic that the Senate continue to meet in person, but he conceded Friday that keeping Republican senators healthy was crucial to the fate of the nomination.

“I think every precaution needs to be taken because we don’t anticipate any Democratic support at all, either in committee or the full Senate, and therefore everybody needs to be in an all-hands-on-deck mindset,” he said in an interview with conservative radio host Hugh Hewitt.

The posturing around the court fight played out as government officials at the White House and on Capitol Hill spent Friday racing to trace those who had come in contact with known carriers of the virus to determine how far it had spread.

Trump was in proximity to Barrett when he announced her nomination in the Rose Garden a week ago at a well-attended celebration where few masks or other precautions were evident. At least two other high-profile attendees, the Rev. John Jenkins, the president of the University of Notre Dame, and Kellyanne Conway, a former White House counselor, said Friday that they had also tested positive.

Lee and Tillis were among at least eight Republican senators present at the White House event, where some guests also gathered indoors and where video captured Lee hugging other attendees without a mask. Tillis wore a mask.

Both men are on the Judiciary Committee and met with Barrett on Capitol Hill this week indoors, without masks, as did more than a dozen others. Tillis’ office released a photograph of the senator and the nominee bumping elbows. Both senators said they felt fine but would isolate for 10 days, placing them on track to reemerge on the day Graham intends to begin Barrett’s hearing.

Other lawmakers who had been in proximity to Trump or his aides said they were getting tested. Among them were Speaker Nancy Pelosi; Sen. Rick Scott, R-Fla.; and Sen. Kelly Loeffler, R-Ga., who all announced they had tested negative.

Republican members of Minnesota’s congressional delegation, who flew with the president on Air Force One from Washington to a campaign rally in Duluth, also said they were being tested.

Rep. Jim Jordan, R-Ohio, flew to the presidential debate in Cleveland on Tuesday on Air Force One with the president and Hope Hicks, a close aide to Trump who tested positive Thursday. Jordan announced Friday that he had tested negative.

Concerns about the outbreak appeared to lead to a change in Congress’s much-maligned approach to testing the thousands of people who stream in and out of the Capitol complex each week, many of them flying in from around the country.

The Office of the Attending Physician informed lawmakers Friday that same-day testing would now be offered in the Capitol to lawmakers who showed possible coronavirus symptoms or had been exposed to someone who had tested positive. Staff members who came into contact with someone who tested positive could also get tests, the office said.

The announcement came after Schumer had expressed deepened anxiety about the health outlook in the Capitol after Trump’s positive test.

“This episode demonstrates that the Senate needs a testing and contact-tracing program for senators, staff and all who work in the Capitol complex,” Schumer said. “We simply cannot allow the administration’s cavalier attitude to adversely affect this branch of government. It is imperative that all results be made public in order to contain a possible outbreak and so we can determine the need for senators and staff to quarantine or self-isolate.”

Fresh fears about the spread of the virus only stiffened resistance to Barrett’s nomination among Democrats, who were already outraged that Republicans were racing to confirm a Supreme Court justice so close to the election after having blocked President Barack Obama from filling a vacancy nine months before Election Day in 2016.

But with Trump’s reelection in doubt and their party in danger of losing its Senate majority, Republicans are even more eager to confirm the nominee quickly. They have insisted they are justified in moving ahead with the nomination because Trump was elected in 2016 and Republicans gained seats in the Senate in 2018, an argument that would be undercut by losses in November.

Some Republican advisers were pushing to scrap plans to keep the Senate in session next week, hoping to reduce the risk of more Republican senators becoming infected. But adjourning may not be in McConnell’s control. He had been in favor of allowing senators to go home, but Democrats trying to inflict pain on Republicans for their rush to fill the Supreme Court seat refused to go along, using parliamentary tactics to prevent it.

As for Barrett, two officials with knowledge of her medical history said that she had already had the coronavirus and recovered this year, potentially providing some immunity for her. But it was not yet clear whether she would continue her courtesy meetings with senators in person next week.

She tested negative for the virus Friday, officials said.