Nope, back to the House where they have to muster 2/3rds to override. Should that happen (not likely, based on passage numbers), then it's on to the Senate where again, it needs 2/3rd to override (again not likely based on passage numbers) Veto will be sustained.
And yes, it will end up in the USSC. But Congress passed a law granting the president the authority, hard to argue against that...