I doubt it. There would be absolutely no justification for filibustering an appointee to VP to serve out the remainder of the term. It isn't anything at all like a lifetime tenure on the federal bench. If the dems were to filibuster the appointment for VP, even the lamestream press would have trouble carrying water for them.
The press would never have trouble helping the dims with anything. But it's irrelevant anyway, as Cheney isn't going anywhere.