Speier added that the transcripts will give the American people "an eye on exactly what we have heard, and what we have heard is growing evidence of grounds for impeachment."

The California Democrat was less specific on when public hearings as part of the impeachment probe will begin, but said they would begin soon.

"I think they're going to begin very soon," Speier said. "We have one more week of interviews that will take place and then I'm pretty confident we're going the move into a public hearing setting in which the House Intelligence Committee, along with the Foreign Affairs Committee and the Oversight Committees, will start to place in the public's hands the information."

House Majority Leader Steny Hoyer (D-Md.) also appeared on CBS on Sunday, and he said Congress will move "relatively soon" to hold public hearings but would not commit to wrapping up those hearings before Thanksgiving.

"Time is not constraining us," Hoyer said. "The truth and the facts are constraining us. We are going to move as soon as the facts and the truth dictate that we have."