No question they're huddling to discuss the feasibility of that right now, like you pointed out. I think they will conclude, however, that they will need something else to make a filibuster a politically viable option.
I'm wondering if we won't see an Anita Hill come slithering out from under a rock sometime tomorrow, just in time to get booked on all the Sunday shows and give the Dims an excuse to demand more hearings?
I don't think the democrats even considered an "anita hill", since Alito is a white guy.