Byrd's argument was similar. That the Senate has no duty to take up the nominee. That is a Constitutional question, and I think the Senate does have a duty - but that is not the point I want to make now.
As a procedural matter, given the nominee is being debated, it may be instructive to view how the Senate handles Nominations and Treaties. We know that Rule XXII (cloture) has been used to dispose of the nominee, when less than 60 votes were obtained to accomplish two things, limit debate, and vote on the candidate.
But what if, instead of looking for a YES vote, we seek a "NO" vote? How many votes would be required to postpone, table, or otherwise dispose of the nominee? Could less than a simple majority kill the nomination with a motion to table? No way! Well then, how is it then that less than a simple majority can kill the nomination otherwise?
In reading Riddick's Senate procedure (in a failed attempt to find the "talk or vote" rule), I noticed that Senate procedure required 2/3rds supermajority to postpone indefinitely, consideration of a Treaty. Likewise then, it would take a simple majority to postpone indefinitely the consideration of a nominee. Not a minority, as the DEMs have been asserting.
Most of the links below relate to "forcing a real filibuster" (I think it is impossible), and can be ignored. The point of this post is citable by only the "Appendix - Forms - and Index" link, the last link just above my closing comments.
http://www.access.gpo.gov/congress/senate/riddick/
Links to Riddick's Senate Procedure
http://www.gpo.gov/congress/senate/riddick/832-842.pdf
Executive Sessions
http://www.gpo.gov/congress/senate/riddick/938-953.pdf
Nominations (see p952)
http://www.gpo.gov/congress/senate/riddick/934-937.pdf
Motion to move the question is out of order
http://www.gpo.gov/congress/senate/riddick/1038-1078.pdf
Quorum call (see pp 1073, 1074)
The appendix has forms and the phrases uttered by the chair. Compare the form of handling a Nomination (starting at page 1521) with the form of handling a Treaty (starting at page 1554). In particular, that for a treaty, a motion to postpone indefinitely (to not act) requires a two thirds majority.
This implies that a simple majority is required to lay aside a nominee, and that less than a simple majority is not sufficient to lay aside the nominee.