I think I know how this is going to end:
Trump declares a state of emergency, The House declares that there is none. By law the Senate has to vote on that within 18 days, and there will be a court challenge. Trump loses at least one of those , probably both (or McConnell refuses to hold a vote and is sued on that and loses at the SC, then loses the vote).
Government opens in the interim, Trump complains about traitors stopping him from building the wall, his base buys his argument whereas Trump hopes low-information voters forget about this in 18 months time.
Honestly its all on Mitch now. Trump can veto whatever he wants, and Congress can override his veto. However, Mitch won't let any bills go on the floor to vote and no Republican has the backbone to do anything about it.