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Calls to allow lawmakers to vote on legislation remotely grew significantly louder on Sunday, after Sen. Rand Paul, R-Ky., announced he had tested positive for coronavirus, and Sen. Mitt Romney, R-Utah, revealed he and other senators recently ate lunch with Paul.

Paul has been in quarantine in Kentucky and continuing to work, while staffers in his Washington, D.C., office have been working remotely for the past 10 days, Fox News has learned. Romney said later that his physician had instructed him to "immediately self-quarantine and not to vote on the Senate floor."

Sen. Mike Lee, R-Utah, also revealed he would self-quarantine late Sunday, although he emphasized he would work as much as possible remotely.

"Coronavirus has now arrived here in the Senate," Senate Majority Leader Mitch McConnell, R-Ky., said on the Senate floor Sunday evening. "There are at least five senators in self-quarantine."

McConnell said a planned 6 p.m. ET proceudral vote on a new coronavirus stimulus bill would go ahead. "We need to signal to the public that we’re ready to get this job done," he said. "And the way to do that is to vote aye in five minutes on cloture on the motion to proceed." (Democrats ultimately shot down the bill by rejecting the procedural vote, angering Republicans who say they're playing politics to secure funding for unrelated measures during a national crisis.)

Fox News is told both members and staff have been livid about why Senate Republicans continued to meet, en masse, and in-person for days as the coronavirus crisis worsened. In addition, some lawmakers from both parties were livid specifically with Paul.

For days, Senate Republicans have met in large numbers in the Mike Mansfield Room in the Capitol, the Kennedy Caucus Room and the Central Hearing Facility in the Hart Senate Office Building. Senate Democrats have conducted most of their meetings via conference call. While other Americans were practicing social distancing, Republicans kept pouring into the same rooms on a daily basis.

"We need to talk with the attending physician," said one senior GOP source, referring to Dr. Brian Monahan, the attending physician for the Capitol. "And, Rand Paul."

Paul became the first member of the Senate known to have been infected with coronavirus, but Reps. Mario Diaz-Balart, R-Fla., and Ben McAdams, D-Utah, also have tested positive, as have at least two congressional staffers.

Sen. Brian Schatz, D-Hawaii, tweeted after Paul's announcement a call for "immediate" procedural changes.

"The responsibility of the Senate is to remain operational," Schatz wrote. "You are not protecting an institution by rendering it unable to function. Remote voting must be instituted immediately, so that the federal legislature can do its job, not just today, but for the duration of this crisis."

He continued: "We may lack a quorum shortly if Leader [McConnell] doesn’t realize the urgency of remote voting. The Senate still has to do its job, but there’s simply no reason we have to do it in a bunch of gilded rooms and infect each other, endangering our ability to pass legislation."

Reps. Ted Lieu, D-Calif., and Elise Stefanik, R-N.Y., echoed Schatz's message.

"I will keep @RandPaul in my thoughts & look forward to him getting well soon," Lieu wrote. "Sen Paul says he was not aware of any direct contact with any infected person. With long incubation, impossible to know who may be carrying the virus. This is why Congress needs to go to remote voting."

Stefanik, meanwhile, wrote that "Congress needs remote voting. Period. Full stop. ... We have 21st century technology and we need to use it to protect our communities now."

Added Dan Pfeiffer, a former top adviser in the Obama administration and podcast host: "The House and Senate need a remote voting plan ASAP."

Pictures began circulating on social media Sunday of Paul eating lunch with other GOP senators on Friday, including Romney.

A spokesman for Sen. Jerry Moran, R-Kan., said Moran briefly saw Paul at the Senate gym Sunday morning and that he shared that information with GOP colleagues at a policy meeting. Moran "followed CDC guidelines and kept a safe distance between him and Sen. Paul,'' spokesman Tom Brandt said. Moran has spoken with the attending physician at the Capitol and has been told he does not need to self-quarantine, Brandt said.

Sen. Marco Rubio, R-Fla., was pictured eating with Paul last Friday, two days before Paul announced his diagnosis. Rubio "shared the duration and nature of his interactions with Senator Paul with the Office of Attending Physician. It was determined they were low-risk interactions that do not require for self-quarantine," a Rubio spokesperson told Fox News.

South Dakota Sen. John Thune, the second-ranking Republican senator, said on the Senate floor that lawmakers will consult with the attending physician about all senators who have been in contact with Paul.

Sen. Dick Durbin, D-Ill., and Sen. Rob Portman, R-Ohio, last Thursday introduced a resolution to amend the chamber's rules to allow for remote voting in emergencies. House Majority Leader Steny Hoyer, D-Md., also said in a letter to fellow Democrats that he expected the House to "adjust our voting procedures" in order to follow Centers for Disease Control and Prevention [CDC] recommendations limiting the number of people in any one gathering.

The resolution introduced by Portman and Durbin would allow the Senate majority leader and the minority leader – currently Mitch McConnell, R-Ky., and Chuck Schumer, D-N.Y. – to agree to allow "secure remote voting" in an emergency. The Senate then would be able to vote every 30 days to continue to allow remote voting.

"In times of a national emergency, the Senate must be able to convene and act expeditiously even if we can’t be together in person," Portman said in a statement. "While I know there is resistance to changing a Senate tradition to allow for remote voting during national emergencies, I believe this is an important issue and worthy of robust discussion among our Senate colleagues."

The Senate was in session Sunday seeking a bipartisan response to the pandemic. If approved, the bill would be the third measure Congress has approved in response to the coronavirus this month.

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The White House increasingly has emphasized that testing should prioritize the elderly and health-care workers who showed symptoms of the virus. While most cases of COVID-19 have been mild and tens of thousands of people have recovered, older people and those with underlying health problems have been at higher risk for more serious problems, such as pneumonia.

“We don’t want everyone to go out and get a test because there’s no reason for it," President Trump told reporters in a briefing last Friday.

Fox News' Tyler Olson, Ronn Blitzer, Jason Donner, Ben Florance, Chad Pergram, Sally Persons and The Associated Press contributed to this report.