Supplemental funding for the war isn't the same as the military budget. Even if all of the extra money disappeared, they'd still have resources to leave, albiet in a way that a Marine in the Korean war once described as "Advancing in the other direction".
It would by far be the most embarassing and televised retreat in American military history. You'd never get a majority of Dems to vote on a cut like that, even if some of them secretly want it, to prove a point.