I'm not convinced it's a bluff. As an outsider looking in, I'm going to tell you how I see this sort of situation.
The Republicans have embraced the Trump way of just accepting you're the bad guy, knowing your diehards will vote for you anyway. Whereas the Democratic members and voters expect responsibility from their party leaders.
So in a shutdown, the Republicans lose nothing, and the Democrats can lose everything.
And the Republicans will all run to their chosen propaganda outlets to cry about how it's Democrats that are causing the shut down because they "refuse to secure our elections" and if course the typical person who doesn't follow politics much will eat it up. :(
The problem with that is that Republicans are always saying that Government doesn't work and the whole system is dysfunctional, so when they turn around and deliberately break it they'll just tell their idiot constituents that they were obviously right the whole time.
Dems should threaten them with a good time. Say, sure, to vote you have to prove you're a citizen... by showing your passport. More than half of these clowns haven't ever left their trailer park towns.