"I cannot surrender my rights under the Constitution to use a majority vote to make the rules of this institution better," said Merkley, who called the steps in the McConnell-Reid deal a "modest step forward."

"I strongly disagree with one thing that was announced here — the idea that the two leaders are taking off the table us utilizing our constitutional rights," said Udall. "That's a good agreement for them; it doesn't apply to 98 other senators. Each senator under the Constitution has his or her right to rely on those constitutional rights."

Sen. Charles SchumerCharles SchumerDean: Schumer's endorsement 'kiss of death' for Ellison How the candidates for DNC chair stack up ahead of Saturday's vote DNC candidate Harrison drops out, backs Perez for chairman MORE (D-N.Y.) also said today he was upset that the deal did not limit filibusters to "talking filibusters." But under Senate rules, it would be almost impossible for senators to change the rules without support from the Senate leadership.

When the Senate returns at 2:15 p.m., senators will debate talking filibusters prior to a series of votes expected Thursday night.