To me this sounds like any agency can use whatever funds the house gives them. They don’t need obama’s signature. After all, he doesn’t actually write the checks. And what could he veto? A budget? There’s not one. Can he veto a CR?
To fund it, the bill would have to be passed by both houses and signed into law by the president. But if the house wants to deny funding, say for an unconstitutional runaway program like obamacare, they simply refuse to pass a bill funding it and there’s nothing the senate or the president can do about it. In other words, the House has the constitutional power to snap shut the purse. Just say no!
And it’s not like there’s any reason to negotiate or compromise. I can’t think of any bill the republicans should be wishing to pass at this time, other than bills repealing or cutting government.