Senator Feinstein’s comments on Face The Nation today (reported in this AP story) would appear to signal clearly that the Democrats won’t have the votes to filibuster Alito’s nomination (and therefore presumably won’t try to):

A Democrat who plans to vote against Samuel Alito sided on Sunday with a Republican colleague on the Senate Judiciary Committee in cautioning against a filibuster of the Supreme Court nominee. “I do not see a likelihood of a filibuster,” said Sen. Dianne Feinstein, D-Calif. “This might be a man I disagree with, but it doesn’t mean he shouldn’t be on the court.”