McConnell's floor speech came a day after Senate Majority Leader Harry ReidHarry Mason ReidMcConnell not yet ready to change rules for Trump nominees The Hill's Morning Report — Sponsored by CVS Health — Trump’s love-hate relationship with the Senate Trump to press GOP on changing Senate rules MORE (D-Nev.) agreed to demands to vote on five Republican amendments to the Export-Import bank reauthorization bill, as well as have a 60-vote threshold on each amendment and on the final bill itself.

The agreement, announced by Reid on Monday, indicated that the Senate avoided an impasse over moving the export-import legislation reauthorization bill, the Securing American Jobs Through Exports Act (H.R. 2072), which passed the House 330-93 a week earlier.

"Now what I and my colleagues have been saying for three years is it doesn't have to be this way," McConnell said. "Give us an opportunity to play a role in the process and we'll work together on bipartisan solutions. Just look at the record: when Democrats blocked all debate and amendments on the Export-Import bank legislation it went nowhere. When they agreed to our reasonable request for input on the bill, that changed. They could've accepted this offer much earlier, but they didn't because it didn't fit the storyline."

McConnell said the situation was similar to recently passed bills on unemployment insurance legislation and postal reform.

"It's the same story every time," McConnell said. "It's the same story every time. Poison pills are removed, Republican input is allowed, and then things happen."

McConnell said when Democrats refuse to let Republicans offer amendments, legislation will have trouble making its way through the chamber.

"There's a lesson here: when both sides have a chance to debate and amend, legislation tends to move," McConnell said. "But when the majority refuses any ideas that they didn't come up with, things slow down. Let's hope this new process will stick."

In response, Sen. Dick DurbinRichard (Dick) Joseph DurbinThis week: House GOP regroups after farm bill failure Overnight Health Care — Sponsored by PCMA — Trump hits federally funded clinics with new abortion restrictions Dem lawmaker spars with own party over prison reform MORE (D-Ill.) said that McConnell was correct "to a point."

"But I might remind the Republican minority leader, what happened last week? We brought up the college student loan bill," the chamber's Democratic whip said. "The object was to make sure that the interest rate on college student loans did not double on July 1, from 3.4 percent to 6.8 percent."

But, Durbin said, when Democrats allowed Republicans to to offer amendments to the student loan bill last week, they still did not vote with Democrats. 

"What we offered on the floor to the Republicans was an opportunity to bring up the measure and they could bring up their amendments to the measure. That, I think, is what the Senate Republican leader just asked for," Durbin continued. "How many Republican senators voted with us to bring up the student loan measure subject to amendment? None. Not one. So this suggestion that we're in filibuster because we don't offer an opportunity for amendment overlooks what happened last week. The college student loan bill gave ample opportunity to Republicans to offer an amendment. And yet they still wouldn't' allow us to proceed to that measure."

So, Durbin continued, the minority party — Republican or Democratic — should be allowed to offer amendments to a bill as long as those amendments are related to the bill.

"It was a good faith offer by the Democratic leader," Durbin said. "I think that we need to find some commonality here where we can offer to the minority — whichever party is in the minority — the opportunity to offer relevant amendments to a bill," Durbin said. "That means, of course, that it's an amendment that relates to the subject matter of the bill."