By ambushing them with the press, POTUS was able to put the ball squarely in their court on live TV. They are now in a no win, no win, no win, no win situation.
If they don't cave and come up with the $5bn, Trump shuts down the gov't and it's on them.
Then he uses the military (national security) to build the wall anyway.
If they cave and give him the $5bm Trump wins, they lose, and their base eats them alive.
Aaand, even if his leverage was declas, he doesn't have to do it himself. He's got Huber and Horowitz to do it for him anyway.
This is a good movie.