Based on past actions of R's it certainly will. There will be no reason for the rats to be afraid of another cloture vote if the R's don't make them pay for it via a 24/7 and the R's will want to avoid future confrontation at all costs. The rats will have grown bolder and think they found a way to run the senate with 40 votes.
It would be a big mistake to table the nomination.
Frist has called for the vote several times, and each time, a DEM Senator has objected.
A motion for a cloture vote has to be filed in advance of the cloture vote, nominally 48 hours before the cloture vote.
At this point, I am indifferent on the need or value to a motion for a cloture vote, and have the feeling the GOP is playing this very well. As you might guess, I am not in the "24/7 now or never" cheering section.