Lawmakers had been questioning Bannon for roughly 90 minutes when questions began on the transition, several sources said. Shortly into that line of questioning, Bannon was cut off by his lawyer, according to the sources. At that point, the interview stopped and the committee issued a subpoena to force him to divulge this information. GOP leaders of the committee would not rule out holding Bannon in contempt for failing to provide information.

Florida Rep. Tom Rooney, a senior Republican on the House Intelligence Committee, said Tuesday that Steve Bannon's testimony is running into problems over whether he can invoke executive privilege for events that occurred during the transition.

"I certainly think that the committee respects executive privilege, it's when does that attach is the question that's sort of dominating the day," Rooney said. "At what time does that attach -- during the transition or during the actual swearing-in?"