The House passed the budget 300 to 128. The Senate passed it 83 to 16. Those are veto-proof margins. If Trump surprises Congress and vetoes the budget (which would shut down the government again), Congress will just override his veto.
McConnell, and others close to Trump are saying that he will now declare a national emergency, and use military and disaster funds to build his wall. Speaker Pelosi has already said she is considering going to court to stop that -- and the Justice Department has warned Trump that the courts are likely to stop the emergency order (at least temporarily).
I think he knows that he won't be able to get away with declaring a national emergency and using funds designated by Congress for other purposes. He just playing a public relations game. He wants to be able to tell his base that he did everything he could to build a wall, but Democrats (and the courts) stopped him.
The fact is -- Trump has lost this fight. There will be no wall -- not this year, and not next year.