The existence or lack thereof of a "budget" is irrelevant, and a "deemed" budget resolution has no legal force any more than the resolution itself does.
The only thing that enables the expenditure of funds is the passage by both houses, signed into law by the president, a bill appropriating funds to be expended. Simultaneously each house must also pass an authorizing bill authorizing the departments to expend funds that are appropriated. Again each of these has to be signed into law by the president. It is a dizzyingly complex process, and this kabuki dance is gone through each year while the taxpayers are fleeced ever and every more by the inability of anyone to actually understand all of this. But it is a well scripted kabuki dance.
That they cannot even pass a budget resolution shows the level of incompetence to which they have sunk, but it is of no legal significance.
there you go...