
That's why programs like this are on a black budget. There's no way to defund it, because it is lumped in with a lot of other black budget stuff that they'll want to keep.
The real choke chain they have on him is to not renew the law that allows him to do this at all. Even the 'illegal' spying that Bush started and Obama continued that was revealed by Snowden was 'legal' based on an interpretation of a law from a White House lawyer that the AG approved. No one in the intelligence or law enforcement community is going to maintain a program spying on US citizens without some law to cover his butt, so if the congress is pissed enough they can uncover his butt and force the program to end.
I'm sure lapdogs like Feinstein and Burr will always vote for whatever spying the FBI wants, but you just need to piss off some of the middle of the road guys to join the odd anti-spying alliance of far right guys who are above all suspicious of government and far left guys who above all believe in civil liberties, and the law won't be renewed next year.