Basically, the argument comes down to this question: Does the "advice and consent" clause obligate the Senate to provide an up-or-down vote on every candidate coming before it? Bruce Regal is quoted as noting:
[The] notion that the Senate acts unconstitutionally when it fails to affirmatively consent or reject within some specified period of time (the end of a session perhaps , or some period set by the President, be it Washington or a successor, etc.) seems incompatible with this ordinary understanding of consent and its opposite, non-consent. If I am asked by my minor child to consent to a contract she wishes to enter into, I may express my decision not to consent either by saying "No" or by simply not acting. The consent required is my affirmative approval and anything short of that, including simple non-action, renders any contract my daughter may sign unenforceable. Whether I have said "No" or not makes no real difference to the enforceability of the contract, although it may make a difference to my daughter because the "No" presumably is a signal ending the discussion between us on the subject, whereas my nonresponsiveness may seem to leave the question open (although eventually she will probably give up asking).
This is an excellent point; but I think it does not go nearly far enough, for two reasons.
First of all, the filibuster deals with only part of the Senate's powers (and, depending on one's interpretation, responsibilities). The clause also requires advice from the Senate, not just consent. In other words, as I've remarked here previously, the clause could just say "consent"; "advice and" would be meaningless. In turn, that means two-way communication between the President and the Senate—which is the only interpretation reasonably consistent with the structure of the clause, of the Constitution's appointment powers, and the Federalist Papers. (Unfortunately, Madison's notes from the convention are less than clear on this issue.) In terms of communication, a filibuster is about as loud a piece of advice short of an explicit nomination list that one can imagine; it represents far more than just a "no" vote, but indicates that a substantial minority (at minimum) of the Senate said "not only no, but hell no!" (One would hope that this is more than partisan pique, but that's the price we pay for a two-party incumbent-dominate system entrenched by first-past-the-post representation.) In that sense, then, a filibuster is a positive embracing of part of the Senate's role under the "advice and consent" clause.
There is another clause elsewhere in the Constitution, though, that sheds some light—and a lot more shadows—on the issue. There is a specific instance in which inaction is treated as a rejection: the pocket veto. One might argue that, since the drafters knew how to provide for a pocket veto, they also would have known to provide for its equivalent under the advice and consent clause. (There's an even better argument, though, that the same drafters who did Article I, § 10, knew how to deal with a "shall not.") In essence, the filibuster against a candidate is a "pocket veto" of the President's nomination. Although the sheer vitriol often present during candidate filibusters is far from elegant, treating the filibuster as a legislative pocket veto has a structural elegance to it, in which the Congress's power to override a veto is balanced by the President's power to make recess appointments. This may be going a bit far afield, though. As if that's unusual in this blawg… or in arguments over appointments… or in Constitutional theory in general.