Just because House Republicans are content to let unemployment insurance run out on 1.3 million people over the holidays doesn't mean the Senate shouldn't try. Let the Republicans filibuster it if they must.
The key here is whether House Republicans will be content to go home without extending unemployment insurance for all the Americans whose help will expire in the coming weeks. We all know the answer to that one is a resounding, boastful yes, but can Democrats bring any leverage to bear to keep it from happening?
The only tool Pelosi would seem to have is refusing to support the budget deal unless a UI extension is included. You can send them all the letters you like urging them to not be bastards about these things, but will the fight be there to actually block them from going home until something is done about it?