A supermajority of the Senate is uniting behind a common goal: Trying to speed up lengthy votes on the chamber floor.

Senators are gathering support for the letter, led by Sen. Thom Tillis (R-N.C.), to allow the Senate's presiding officer to close a vote if one of the letter's signees would be the last member to vote and their vote wouldn't change the outcome.

"As you know, despite our collective efforts to encourage members to vote on the Senate floor in a timely manner, votes are often left open well beyond the allotted time, frustrating a majority of members from both sides of the aisle. Often, the outcome of the vote is not in doubt," senators write in the letter.

A signee to the letter, which is being sent to Majority Leader Charles Schumer (D-N.Y.) and Minority Leader Mitch McConnell (R-Ky.), could also request that a vote be held open, giving themselves an out if needed.

Tillis is still collecting signatures, but the letter has 68 signees so far: 35 Republicans and 33 Democrats.

The letter comes as frustrations over increasingly lengthy Senate floor votes have boiled over into the public this week.

Sen. Kyrsten Sinema (D-Ariz.) was caught on a hot mic on Tuesday remarking dryly, "This is so fast," after she closed a vote that lasted nearly an hour.

Sinema was overheard by a Bloomberg reporter later in the day chiding Schumer for the long votes, reportedly asking "Could we have some discipline in the votes, ever?” and telling the New York Democrat "You’re in charge!”

Sen. Bob Menendez (D-N.J.) was also overheard complaining to an aide as he left the chamber on Wednesday, saying that he's "never seen a more inefficient process in the world," while Sen. Susan Collins (R-Maine) called it "ridiculous."

Sen. Dick Durbin (D-Ill.), Schumer's No. 2, asked Sen. Tammy Baldwin (D-Wis.), who was presiding over the Senate, during an afternoon series how long the previous vote had lasted. Baldwin informed him it had lasted for 55 minutes. He also asked for the name of the last senator who voted, but Baldwin was told by Senate floor staffers that they didn't have that information.

Schumer did make a plea to senators on Wednesday to try to speed up the votes.

"All of us want to get them done in a timely manner to respect the schedules of our colleagues. So in order to move things along, I am urging my colleagues to be ready to vote early when each vote is called, so we can prevent extended delays," he said from the Senate floor.

But votes still dragged throughout the day.

Senators were instructed to stay in their seats to try to speed up an evening series of back-to-back votes — instructions that were ignored by many. The first vote lasted roughly 47 minutes.