"We need a change in the Senate rules to address our broken judicial process," Udall said Wednesday. "I urge all of my colleagues to consider this proposal fairly and without partisan interests."

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Under the New Mexico Democrat's legislation, a judicial nomination that hasn't been taken up by the Judiciary Committee within 180 days would automatically get a cloture vote on the Senate floor.

The proposal would also require a vote on judicial nominees who are on the Senate calendar 180 days, or roughly six months, after they were nominated by the president. Udall is expected to file the legislation on Wednesday or Thursday.

The push to crack down on who decides when the Senate votes on judges comes as Democrats try to keep a spotlight on Garland's stalled nomination.

Udall, pointing to the stalemated fight, said a "line has been crossed [and] this level of obstruction will only get worse for the years to come."

"This isn't governing," he said. "It's an unprecedented power play."

Senate GOP leaders have remained adamant that they will not take up Garland's nomination, despite a steady stream of pressure from Democrats and outside groups.

Asked about a potential lame-duck confirmation, McConnell laughed before saying, "We've already made it very clear that a nomination for the Supreme Court by this president will not be filled this year."