As Republicans expressed hope Sunday that President Donald Trump will know better next time, House Intelligence Committee Chairman Adam Schiff said Sunday that it is "remarkable" that some in the GOP have been saying the House "proved its case," but still do not think the president should be removed from office.

"What's remarkable is you now have Republican senators coming out and saying, yes, the House proved its case," Schiff, the lead House impeachment manager, told CBS' "Face the Nation." "The House proved the corrupt scheme that they charged in the articles of impeachment. The president did withhold hundreds of millions of dollars from an ally to try to coerce that ally into helping him cheat in the next election."

"That's pretty remarkable when you now have senators on both sides of the aisle admitting the House made its case and the only question is, should the president be removed for office because he's been found guilty of these offenses?" he continued.

Schiff's comments came days after the Senate voted against bringing forth additional witnesses, such as Trump's former national security adviser John Bolton and acting chief of staff Mick Mulvaney, and documents in the trial. Only two Republicans, Sens. Mitt Romney, R-Utah, and Susan Collins, R-Maine, voted in favor of witnesses.

Sen. Lamar Alexander, R-Tenn., said he did not support voting in favor of witnesses because the House had "proved" that Trump linked nearly $400 million in aid to Ukraine with investigations he sought into former Vice President Joe Biden, his son Hunter and the Democrats, and that extending the trial was unnecessary. Meanwhile, Sen. Marco Rubio, R-Fla., wrote in a Medium post that simply "because actions meet a standard of impeachment does not mean it is in the best interest of the country to remove a President from office." And Sen. Rob Portman, R-Ohio, criticized Trump's conduct as "wrong" but said it was not worthy of impeachment.

The Senate is expected to acquit Trump this week. Early Sunday morning, Trump, who called his July 25 phone call with Ukrainian President Volodymyr Zelenskiy that led to his impeachment "perfect," tweeted that Democrats "don’t want justice when pushing the Impeachment Hoax, they only want to destabilize the Republican Party so they can do better in the 2020 election," adding, "They are playing with the people by taking it this far!'

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Speaking with NBC's "Meet the Press," Alexander said Trump "shouldn't have" withheld aid to Ukraine and pursued investigations into Democrats the way he did.

"I think it was wrong," he said. "Inappropriate was the way I'd say — improper, crossing the line. And then the only question left is who decides what to do about that."

"I think what he did is a long way from treason, bribery, high crimes and misdemeanors," he added. "I don't think it's the kind of inappropriate action that the framers would expect the Senate to substitute its judgment for the people in picking a president."

Alexander and Sen. Joni Ernst, R-Iowa, both expressed hope that Trump wouldn't do the same again now that he's gone through impeachment.

"I don't think so," Alexander said when asked if he had any reason to believe Trump would engage in the same conduct moving forward. "I hope not. Enduring an impeachment is something that nobody should like. Even the president said he didn't want that on his resume. I don't blame him. So, if a call like that gets you an impeachment, I would think he would think twice before he did it again."

"What example in the life of Donald Trump has he been chastened?," Chuck Todd asked in response.

"I haven't studied his life that close," Alexander said, adding that "hopefully he'll look at this and say, 'OK, that was a mistake, I shouldn't have done that. I shouldn't have done it that way.'"

The retiring senator said Trump should've called Attorney General William Barr instead of the Ukrainians if he wanted an investigation of the Bidens.

"Maybe he didn't know to do it," Alexander said, adding that wasn't "an excuse" for Trump's conduct.

On CNN's "State of the Union," Ernst said she believes Trump "knows now that, if he is trying to do certain things, whether it's ferreting out corruption there, in Afghanistan, whatever it is, he needs to go through the proper channels."

Ernst said Trump's discussion with Zelenskiy was "maybe not the perfect call."

Schiff said that to describe Trump's conduct as "merely inappropriate" is understating the consequences.

He added that such characterization "doesn't begin to do justice to the gravity of this president's misconduct, misconduct that I think undermined our national security as well as that of our ally and threatens the integrity — the integrity of our elections."