Congress was trying to fool with the Powers of the President but I did find a statement that says the President has separate Powers in regard to surveillance on the FISA site. I will go back.
Executive Orders by the President is an issue in which Congress does not and cannot interfere. If they could, you can be darn sure they would want to review each case themselves.
Congress is a "messy place". It is why we wound up with a President with special Powers. We expect all our Presidents to be "moral" and protect our Nation and the danger (I believe according to John Adams) is not a King but a Congress who effectively shuts down the government because of their individual interests.
It depends on the order. The surveillance orders recapitulate statutory language, and are therefore not bothersome to Congress. But Congress did circumscribe Lincoln's suspension of habeas corpus (not that he followed their grant, and not that he thought he needed it anyway).
Others have posted, at some point, executive initiative becomes a political issue. There will be much invasion of privacy as the public will accept.