McConnell's move paves the way for a vote as soon as Wednesday to formally cut off debate, unless senators agree to hold the vote sooner. Republicans want to wrap up the National Defense Authorization Act (NDAA) by the end of the week.

ADVERTISEMENT

Senators could still try to reach a deal to hold amendment votes but that would require the sign off of every senator — an uphill climb in the GOP-controlled Senate. Any attempt to get a vote on one amendment would also likely spark similar calls on the nearly 600 amendments that have been filed to the NDAA.

The move would mark a significant step for Democrats because they would be blocking a bill that has passed for nearly 60 years in overwhelmingly bipartisan votes.The bill also authorizes funding for projects in many of their home states.

"I'd like to have it not get a vote," he said.

To block the bill, if every senator voted, they would need 41 members agreeing to not advance the NDAA until they were able to force a vote on the Iran amendment.

Udall said he voted against starting debate because they didn't have a commitment that the Iran amendment would receive a vote.

“It would be the height of irresponsibility, and a true abdication of our constitutional duty, to finish the NDAA while blocking a vote on our urgent, bipartisan amendment to prevent an unauthorized war. … The Senate cannot duck this vote, and Majority Leader McConnell should honor his commitment to an open amendment process. We cannot do our constitutional duty without one," Udall said in a statement.

—updated at 12:30 a.m.