Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellGraham: GOP will confirm Trump's Supreme Court nominee before the election Trump puts Supreme Court fight at center of Ohio rally The Memo: Dems face balancing act on SCOTUS fight MORE (R-Ky.) on Tuesday blocked an attempt by Sen. Rand Paul Randal (Rand) Howard PaulSecond GOP senator to quarantine after exposure to coronavirus GOP senator to quarantine after coronavirus exposure The Hill's Morning Report - Sponsored by National Industries for the Blind - Trump seeks to flip 'Rage' narrative; Dems block COVID-19 bill MORE (R-Ky.) to allow for temporary remote voting as the House prepares to take up its own proposal this week.

Paul, speaking from the Senate floor, argued that Congress should either return to session or allow for remote voting to be temporarily available during emergencies.

"If there exists too much danger to have Congress meet in person, we should allow emergency voting remotely," Paul said from the floor.

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But McConnell objected to Paul's attempt to pass his resolution, which would allow for any senator to try to get up to a 30-day temporary approval for remote voting.

"Senator Rand Paul offered an amendment to allow remote voting if necessary. He believes Congress should at once return into session, if not remote voting should be available during emergencies," said Sergio Gor, a spokesman for Paul.

McConnell and other members of GOP leadership have indicated that they remain opposed to remote voting. The Senate is currently in the middle of a five-week break sparked by the coronavirus, but before members left, the GOP leader shot down a question about allowing for senators to vote from outside the Capitol.

“We’ll not be doing that. There are a number of different ways to avoid getting too many people together,” McConnell told reporters.

Instead, the GOP leader implemented social distancing techniques, including allowing for longer votes and encouraging members not to linger on the Senate floor. The effort was met with mixed success, as several senators were spotted standing shoulder to shoulder or chatting in tight groups.

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Paul's attempt to implement remote voting comes as Sens. Dick Durbin Richard (Dick) Joseph DurbinTumultuous court battle upends fight for Senate McConnell focuses on confirming judicial nominees with COVID-19 talks stalled Senate Republicans signal openness to working with Biden MORE (D-Ill.) and Rob Portman Robert (Rob) Jones PortmanMcConnell locks down key GOP votes in Supreme Court fight Romney undecided on authorizing subpoenas for GOP Obama-era probes Congress needs to prioritize government digital service delivery MORE (R-Ohio) have offered their own rules change resolution. Sens. Roy Blunt Roy Dean BluntThis week: Supreme Court fight over Ginsburg's seat upends Congress's agenda McConnell locks down key GOP votes in Supreme Court fight Murkowski: Supreme Court nominee should not be taken up before election MORE (R-Mo.) and Amy Klobuchar Amy KlobucharBattle lines drawn on precedent in Supreme Court fight Sunday shows - Ruth Bader Ginsburg's death dominates Klobuchar: GOP can't use 'raw political power right in middle of an election' MORE (D-Minn.), the chairman and top Democrat on the Senate Rules Committee, are also working on a deal on remote hearings.

House Democratic leadership, meanwhile, has embraced the idea of voting by proxy.

The House is expected to vote this week on changing its rules to allow members to vote remotely during the coronavirus pandemic.

“The House is expected to vote on a rules change related to remote voting by proxy,” House Majority Leader Steny Hoyer Steny Hamilton HoyerWhite House opposes House energy bill as Democrats promise climate action This week: Supreme Court fight over Ginsburg's seat upends Congress's agenda House Democrats postpone vote on marijuana decriminalization bill MORE’s (D-Md.) office said in a notice to members.