Sen. Chuck SchumerCharles SchumerHow Trump can score a big league bipartisan win on infrastructure Overnight Finance: Dems introduce minimum wage bill | Sanders clashes with Trump budget chief | Border tax proposal at death's door GOP senators distance themselves from House ObamaCare repeal bill MORE (D-N.Y.) on Tuesday offered a proposal to fix what he admitted is a Senate that is failing to legislate.

"On both sides of the aisle, there's a great deal of consternation that we're not legislating," Schumer said on the Senate floor. "We've had this problem for a while, and Thursday it came to a head, there were some harsh words that were issued by some."

Schumer was referring to Thursday's blowup between Republicans and Democrats after Majority Leader Harry ReidHarry ReidGOP frustrated by slow pace of Trump staffing This week: Congress awaits Comey testimony Will Republicans grow a spine and restore democracy? MORE (D-Nev.) said he would not allow any amendments to a bill extending emergency unemployment benefits.

Schumer suggested that the two parties find a way to embrace the traditional roles of Senate majorities and minorities in order to allow the Senate to function again. He said involves ensuring that the minority is allowed to offer amendments, and the majority is allowed to get an up or down vote on legislation once the amendment process is over.

"Certainly, the minority should get to offer amendments," Schumer said. He said there are details within that statement that need to be worked out, such as whether the minority should be allowed to offer unlimited, non-germane amendments.

"But other side is that the majority should be able, once the amendments are disposed of, to get an up or down vote on the final passage of the bill," he added. "If friends of the other side of the aisle say, 'I want to offer my amendment, but unless it passes, I am going to vote to block the bill from coming up for an up or down vote,' that doesn't seem right."

Schumer said Democrats are expected to discuss ways to unclog the Senate at their caucus lunch Tuesday, and said his impression was that Senate Republicans would be discussing the same issue.