GOP Sen. Lindsey Graham on Monday said he "totally" supports the "idea of remote voting so the Senate can continue to operate during this crisis."

Graham's comments come at a time when the GOP is at risk of losing its majority in the Senate as an increasing number of lawmakers self-quarantine.

Republican Sen. Rand Paul on Sunday announced he tested positive for coronavirus, and he's been in close proximity with other GOP senators in recent days.

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Republican Sen. Lindsey Graham on Monday said lawmakers should be able to vote on legislation remotely.

"I totally support the idea of remote voting so the Senate can continue to operate during this crisis. We should make this change before the Senate leaves town," Graham tweeted.

This came as an increasing number of members of Congress have become infected with coronavirus or exposed to someone who's tested positive, and therefore have gone into quarantine and cannot vote in person.

GOP Sen. Rand Paul on Sunday announced he'd tested positive for the novel coronavirus

Congress has already passed two bills in response to coronavirus, and was debating over a third on Monday. At least five Republican senators were self-quarantining as of Sunday, and as a result, missed a key procedural vote on coronavirus legislation Sunday evening. The $1.6 trillion emergency rescue package failed to get the 60 votes necessary to move forward, with Democrats standing in the way over concerns that under the current language of the bill too much money is going to corporations and not enough to workers.

If more Senate Republicans go into quarantine, and remote voting is not permitted, this could effectively result in the GOP ceding its majority in the chamber to Democrats. Republicans have 53 seats in the Senate, while Democrats have 45 (and two Independents caucus with the Democrats). With five Republicans quarantined, the GOP has a very slim majority (48-47) and is more reliant on Democratic support to move legislation forward.

But it might take some time for remote voting to occur, given changing rules in Congress can be tedious and could require a vote, among other potential challenges.

"There are people who want us to move forward on remote voting and there are others who have hesitation, which probably means that if you're trying to make that kind of change, it would require votes," House Rules Committee Chairman Jim McGovern told CBS News on Sunday.

Almost 70 House Democrats on Monday formally requested that rules be changed so lawmakers can vote remotely during national emergencies such as the coronavirus pandemic.

"Unfortunately, during such circumstances, requiring members to vote in person may pose public health risks or even be physically impossible for persons under quarantine. We need to provide a mechanism through which Congress can act during times of crisis without having to assemble in one place," the lawmakers wrote in a letter to McGovern.