I think I've figured out what passes for a "strategy" behind Drumpf's threat to extend the shutdown for weeks or months. It doesn't have much to do with the border wall, but instead with the part of government he has proven unable to control. On Friday 11 Jan 2019 (or shortly thereafter), the federal courts will run out of money for ordinary operations and be restricted to hearing priority matters. Criminal cases count as priority matters. Civil rights cases, however, do not.
So over the weekend and early next week, I thoroughly expect some really outrageous Drumpf Administration executive orders, regulations, etc. (presuming we can distinguish this from business as usual day under this administration), followed very quickly by lawsuits from the Usual Parties. Followed even more quickly by cut-and-paste orders from the respective Offices of the Clerk staying the lawsuits "until further order of this court." Too, this means that the anti-ACA ruling from a district court in Texas will not be proceeding through the appellate process, because it's not even conceivably a priority action.
Next, Alton Brown will devote an entire episode of a program to Coronation Chicken. It's been mentioned in passing regarding the White House and shutdowns before, but it was developed as a cheap festive dish in Blighty after the Second Thirty Years' War (using cheapo "curry powder" because fresh herbs and spices weren't available — or at least not affordable). Which seems all too appropriate with Brexit looming… Of course, that reference to The West Wing will backfire because the Executive Branch was the good guys, and nobody near where the border wall belongs will look at the substance.