Definitely. I think that would be very hard to carry out for various reasons, though. Intelligence agencies generally want minimal oversight and more power so you'd be fighting that at every corner which includes:

1) Vague threats to leak/expose Congress members' personal matters who craft legislation against them. Chuck Schumer (a sitting US senator) admitted on live TV that the intel community has "six ways from Sunday" to get back at you.

2) Blatant disregard for the law by "just following orders", see anecdotes about Michael Hayden, a former CIA director.

3) Data storage, backup, and classified systems. Decades of collection probably means this data is scattered in many places which could give these agencies a chance to retain data "accidentally" or put up roadblocks due to high level clearances being required to work with these systems.