It will likely end one of two ways. An increasingly demented Trump could go ahead and declare a national emergency, order the military to build the wall—and his order will end up being quickly reviewed by the Supreme Court.
It’s not quite a slam-dunk that the Court would approve it, because Chief Justice Roberts is showing signs of disgust with Trump’s extra-constitutional tendencies. To the extent that Trump listens to political advisers at all, he’s being told that this is a really bad idea.
Just as likely is the possibility that more Republican senators will defect. As recent public comments suggest, such GOP senators as Pat Roberts of Kansas, Mitt Romney of Utah, Shelly Moore Capito of West Virginia, as well as several other senators up in 2020 such as Cory Gardner of Colorado and Susan Collins of Maine are very unhappy about the shutdown.
They would much prefer to continue the fight about the wall in a separate ring of the circus, while the rest of the government re-opened. This happens to be the Pelosi-Schumer position, and as the shutdown drags on, the risk of more Republican defections continues, leaving Trump to play the weaker hand.
The end-game could be very well be some sort of fig leaf that Democrats can call border security and Trump can call a barrier. But with Trump, you never know. He might invade Mexico. Or Canada.