But the resolution faces an uphill battle in a GOP-controlled Congress, with both the Trump administration and Republican leadership opposed to the effort.

Murphy also appeared somewhat cautious about whether or not his resolution would be able to muster the votes. He predicted most Republicans will oppose it while the vote count remained "fluid" on the Democratic side.

"You know it's a new precedent. ... I think a lot of members on our side are tying to figure out what a 'yes' vote means and what a 'no' vote means," he told The Hill.