Washington — House Intelligence Committee Chairman and lead impeachment manager Adam Schiff says he doesn't see anything Democrats could have done differently in President Trump's impeachment trial, after the Republican-led Senate voted against allowing new witnesses and documents.

Schiff, speaking on "Face the Nation" on Sunday, noted that some GOP senators, like Senator Lamar Alexander, conceded that the House managers proved their case against the president. The Senate voted against calling witnesses and documents Friday night in a 49-51 vote, with only Republican Senators Mitt Romney and Susan Collins siding with Democrats.

"Look, there's nothing that I can see that we could have done differently, because as the senators have already admitted, we've proved our case. We proved our case," Schiff said.

The president's attorneys and some Republicans have argued that Democrats should have subpoenaed former national security adviser John Bolton during the initial impeachment inquiry, but chose not to do so. Schiff declined to say whether the House plans to subpoena Bolton, whose reportedly writes in his forthcoming book that the president did indeed link Ukraine aid and investigations into the Bidens, and directed Bolton to become involved in the Ukraine scheme.

"I don't want to comment at this point what our plans may or may not be with respect to John Bolton," Schiff said, adding that whatever happens, more and more details from Bolton and others will emerge.

The lead impeachment manager also dismissed a statement from Republican Senator Lisa Murkowski, who said the Senate had failed in its responsibilities when announcing her vote against new witnesses.

"They're not mere spectators here," Schiff said of Murkowski and other Senate Republicans.

Schiff said calling the president's conduct merely "inappropriate," as Alexander did in a lengthy statement, "doesn't begin to do justice to the gravity of the president's misconduct."

Whatever happens in the Senate on Wednesday, when lawmakers are set to vote for acquittal, Schiff said it still matters that the president was impeached in the House.

"I still think it's enormously important that the president was impeached because the country is moving away from its democratic ideals," Schiff said.