Since a big chunk of the proposed wall would fall under the 9th Circuit Court, it wouldn’t even need to go as far as the SCOTUS. The 9th has repeatedly blocked unconstitutional actions by Dolt 45, often using his own words against him. In this case, he’s shot himself in the foot, legally speaking, by repeatedly threatening to use emergency powers or the military to fund the wall if it wasn’t put in the budget.
Strategically, the quickest way out of the current shutdown impasse would be for 45 to declare the state of emergency, opening the way for the budget to pass without funding for the wall. Which would then be immediately challenged and blocked as an unconstitutional end-around of the legislative process.
I give it about a 40% chance that this is what Lindsey Graham is angling for. He’s a shitweasel, but he’s also too smart to think that an emergency to fund the wall would be anything but a judicial non-starter.