FBI Director James Comey already went before Congress and was rejected. I'd say the possibility of him succeeding in the future is even lower, given the way this case has played out. He effectively tried to make an end-run around the legislature by going through the courts with an extremely old law. The powers in Congress did not appreciate this at all and had a lot of very pointed questions for him at his last hearing before the House Judiciary Committee[0].
[0] http://qz.com/628745/i-have-no-idea-the-fbi-director-at-the-...