As both a big fan of Tom Geoghegan and a sworn enemy of the filibuster, I wish I could join Kevin Drum in agreeing with his recent argument that the filibuster is unconstitutional. But, alas, I can't. The case for the constitutionality of the filibuster is very strong: Not only does the text of the Constitution not prohibit it, but Article I gives the Senate the plenary power to "determine the rule of its proceedings," as Geoghegan concedes. This doesn't end the debate, but it certainly puts the burden of proof on those arguing that the filibuster is unconstitutional.
Geoghegan essentially raises two arguments. The first of these is originalist: "the ever-present filibuster threat has made the Senate a more extreme check on the popular will than [the Framers] intended." Not only is this an originalist argument, but it's originalism in its most vulgar form, focusing not on what the framers wrote but on their subjective intentions, an argument that not even Antonin Scalia believes should carry weight. I'm not an originalist at all, so I can't really endorse this argument, especially given its rather dangerous implications. The framers probably didn't intend the Constitution to facilitate something like the 20th century regulatory state, either.
More promisingly, he also makes a structural argument, claiming that we can infer from the text that only a majority votes should be required to pass legislation. I think this is correct, as far as it goes, but the problem is that there still is a majority rule in this sense. If 50 Senators and the vice president were to vote for health-care legislation on the merits, it would pass. It's true that, as a practical matter, the difference between the vote to cut off debate and votes on the merits has become largely formal, but when we're dealing with constitutional law such formalities are very important. If we abandon them, we would run into the same problem as Byron York: The argument proves too much. If the argument is true, then the committee system -- which allows fewer than a dozen members to prevent a vote on the merits -- must also be unconstitutional. Moreover, once we go beyond the formal distinction between votes on the merits other votes, the originalist arguments vanish: to argue that James Madison was an opponent of counter-majoritarianism per se (as opposed to a general supporter of majority voting rules) would be crazy.
The filibuster is a blight on American political institutions, and should be abandoned. But, like many bad policies, it's not unconstitutional.