Ultimately they do, by refusing to fund them. There will be a supplemental appropriation up passage in the February time frame.
They have the power, but hopefully not the cojones to use it.
However something like the Cape Cod Orca's bill to deny authorization for any increase in troops would be vetoed, and there's not the votes to override. With the appropriation, it's different, because Bush can't veto what is never passed, and it would be difficult to veto a bill that had some appropriations in it, even if much less than needed.
The President has some flexibility in spending money already appropriated and authorized, but to do so would mean disrupting the process throughout the military. IOW, he move funds from say, training to operations, as both are "Operations and Maintenance" funds. He could delay refurbishment of equipment, but that's a very short term solution, as the equipment is needed, as is the training, for to sustain the forces.