After a historic vote in the House that approved rules for the next steps in the impeachment inquiry of President Trump, Representative Adam Schiff denied accusations by Republicans that the rules are unfair.

"The rules are very much the same as they were during the Nixon impeachment, during the Clinton impeachment," Schiff told "CBS Evening News" anchor Norah O'Donnell. "All they have to argue is process and even the president has acknowledged that's a failure."

Lawmakers voted mostly along party lines to approve the resolution that authorizes the House Intelligence Committee to hold public hearings. It's only the third vote of its kind.

All Republican members voted against it and prior to the vote, denounced what they called a "Soviet-style" nature of the investigation.

"Maybe in the Soviet Union, you do things like this where only you make the rules, where you reject the ability for the person you're accusing to even be in the room," said House Minority Whip Steve Scalise.

Republicans have also raised concerns that Democrats will block witnesses.

"We've asked them for proffer about which witnesses they think are relevant, and I have to say we have concerns that they're going to propose a bunch of witnesses that have no bearing that they can use merely to smear the president's opponents or for other improper purposes," Schiff said.

Ahead of Thursday's vote, House members have been listening to closed-door testimony from key witnesses, including Tim Morrison, the outgoing senior director of European and Russian affairs at the National Security Council and a deputy assistant to the president. Morrison listened to Mr. Trump's phone call with the president of Ukraine, which is at the center of the impeachment inquiry.

Another official who heard that call is Lieutenant Colonel Alexander Vindman, who testified this week. Schiff would not comment on the details of his deposition. But he expects transcripts of closed-door depositions to be released to the public by "early next week."

"I think the public will see that the process has been fair. Both sides have had ample opportunity to question the witnesses. I think they will see facts that cause them great concern about the president abusing the power of his office," Schiff said.

Schiff said he's also concerned about "the president's threats" to the whistleblower who brought attention to Mr. Trump's call with Ukraine's leader.

"I've made it clear to all the colleagues on our committee that we will not be a part of and we will not permit questioning that is designed to out this whistleblower so that the president can exact political retribution," Schiff said. "I would hope that members on both sides of the aisle would be speaking out about the need to protect whistleblowers, this one and others."