Schumer had no leverage. If the budget had not passed, Musk and DOGE would have used that as a excuse to purge even more government employees.
I don't know if Schumer had other motivations or if he just made the biggest blunder of his political career, either way it has not turned out well for him—not only are people actively calling for him to be replaced, it's clear that history will not remember this supposedly necessary shut down prevention as something "heroic".