Just combine these two links please:
1) TPM explains the procedural (and moral) aspects of the so-called 'nuclear option' — in which a parliamentary device would be used to end-run a Senate rule that entrenches [requires a super-majority to change] the filibuster. Using the spurious claim that the filibuster is unconstitutional, Sen. Frist would try to overturn the rule by majority vote.
SEN. SCHUMER: Isn't it correct that on March 8, 2000, my colleague [Sen. Frist] voted to uphold the filibuster of Judge Richard Paez?
Senator Frist's eloquent reply must be read in its entirety.
As for the underlying issues, as I've said before, I don't in principle much like the filibuster. It's anti-majoritarian, albeit in a way that might sometimes counterbalance the built-in tilt of the Senate towards large open spaces. Yes, there can be a value to mechanisms that respect the intensity of feelings of a minority; even so, the filibuster has an ugly pedigree.
I also don't have warm fuzzy feelings for entrenchment of rules regarding unequal democratic representation or apportionment (I'm ok with entrenching individual rights) — like for example the rule that entrenches two senators per state regardless of population disparity. Nevertheless — while I claim no expertise on this question — my gut reaction is that I don't think that entrenching a Senate rule is unconstitutional either.
One thing I am sure about: neither the advise and consent clause nor any other part of the constitution 'requires that a nominee be given an up or down vote'. Whether or not the filibuster is morally valid, or even beneficial in the long run, for my money it is undoubtedly constitutionally valid.