It doesn't matter if they still have money on the books.
If the House will not authorize it's expenditure, via some legislative means...CR, Budget etc. the money cannot be spent.
Bundle all spending authority into a giant CR, and PRECLUDE spending on any of the Amnesty BS. They know how to word this.
The Senate and POTUS can bitch...they can stand up and say the US Government is going to default...SS won't be paid...military won't be paid...NO MONEY FOR ANY MILITARY OPERATION...because they won't sign the House bill.
In this political climate that would be suicide for ALL Democrats.