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Members of both the House of Representatives and the Senate are pushing to allow Congress to vote remotely as leaders work feverishly to hash out an agreement for a massive coronavirus relief bill and after two colleagues tested positive for the novel coronavirus Wednesday.

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

"I joined with Sen. Portman of Ohio in proposing that we take into consideration the fact that we have critically important work to do in the Senate," Durbin said in floor remarks Thursday. "But gathering in groups, as we've done historically, poses a health risk not just to us as members and our families, but to the staff as well as their families."

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He continued: "Why is it required that we be physically present on the floor closer to one another than perhaps we should be at this moment of a public health crisis?"

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

Rep. Mario Diaz-Balart, R-Fla., and Rep. Ben McAdams, D-Utah, on Wednesday were the first two members of Congress to announce they tested positive.

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McConnell, an old-fashioned Senate parliamentarian, panned the idea of remote voting Tuesday, saying he would work to keep senators from spreading the coronavirus among each other "without fundamentally changing Senate rules."

The Senate majority leader said one of the ways this could be accomplished is by extending the amount of time each vote lasts, thus allowing senators to space out their time in the chamber and maintain social distancing.

It is also unclear how "secure" remote voting from members of Congress would work under Durbin and Portman's proposal.

In floor remarks Thursday, Portman also cited constitutional concerns as a reason why he thought the Senate should allow for remote voting.

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"It's important to me, and I think to all of my colleagues, that Article I be heard, that the legislative branch be heard, that we have the ability to convene for the continuity of government and not allow what we would normally do perhaps to shift over ... to the executive branch or not to be addressed at all," he said.

Durbin, citing evolving national security threats worldwide, said it may be inevitable that the Senate figure out a way to have members vote remotely.

"We live in an age where national emergencies, public health crises and terrorism can threaten the ordinary course of Senate business," he said in a statement. "We need to bring voting in the Senate into the 21st century so that our important work can continue even under extraordinary circumstances. Bob Dylan was right: ‘the times they are a-changin'.'"

Fox News' Chad Pergram contributed to this report.