On its face, the problem with the filibuster is that it’s anti-majoritarian. But taking a broader view, the normative status of majority rules is pretty questionable. The bigger problem is that it undermines democratic accountability. Ezra Klein points out that David Obey smartly mentioned this in his retirement announcement saying “All I do know is that there has to be more to life than explaining the ridiculous, accountability destroying rules of the Senate to confused, angry, and frustrated constituents.”
This is related to the unfashionable-in-elite-circles case for strong party discipline. The point is that accountability is maximized when it’s relatively simple for ordinary people to deploy the means at their disposal (voting, or not) to effectuate their ends (throwing the bastards out, or not). When you combine majoritarian legislative procedures with strong party discipline, then all a voter needs to do is (a) remember which party is in charge, and then (b) decide if he likes what’s going on. But thanks to the filibuster, if you don’t approve of policy outcomes you’re likely to blame the majority party even if the outcomes are actually being determined by a minority.