President Donald Trump has criticized, mocked and derided House Intelligence Committee Chairman Adam Schiff on several occasions since taking office, but Democrats said the president crossed a line on Sunday, characterizing one of his tweets about the California Democrat as a "threat."

"Shifty Adam Schiff is a CORRUPT POLITICIAN, and probably a very sick man," Trump tweeted. "He has not paid the price, yet, for what he has done to our Country!"

Schiff, the lead House impeachment manager in the Senate trial of the president, mentioned the tweet during an appearance on NBC News' "Meet the Press." Defending his decision to cite a report during his arguments before the Senate that Trump had threatened Republicans who did not stand with him, Schiff said Trump was "wrathful and vindictive president."

"I don't think there's any doubt about it. And if you think there is, look at the president's tweets about me today, saying that I should pay a price," Schiff said.

"Do you take that as a threat?" host Chuck Todd asked.

"I think it's intended to be," Schiff replied.

White House press secretary Stephanie Grisham told Fox News that Schiff's characterization of the tweet as a threat was "ridiculous."

"The fact that he said that – that was grandstanding," Grisham said on "Media Buzz."

Grisham said Trump is a "counterpuncher" who "speaks in very unique ways" and says "what's on his mind." Though she said she had not spoken to the president about the tweet, she assumed he meant Schiff "hasn’t yet paid the price with the voters."

Schiff's fellow Democratic House impeachment managers also thought Trump's tweet went too far.

"I would just say to the American people, this is totally inappropriate. It is totally a threat, if you will, against the process of this investigation and of this trial," Rep. Val Demmings, D-Fla., said Sunday when asked about the tweet on MSNBC.

"We are defenders of the Constitution," Demings said, vowing that the impeachment managers would do their job "regardless of what inappropriate comments" or "threats that come out of the president."

"He really ought to get a grip and be a little more presidential," said Rep. Zoe Lofgren, D-Calif., on CNN's "State of the Union" on Sunday.

"The president has a tendency to say things that seem threatening to people," Lofgren said. "Adam Schiff is doing his job."

Sen. James Lankford, R-Okla., said on "State of the Union" that, like Grisham, he thought Trump was implying Schiff "will be paying a price at the ballot box" and did not intend it as "some kind of intimidation."

"I don't think he's encouraging a death threat," Lankford said when asked if he was concerned that the president's tweets could inspire violence.

Lankford said he was more offended by Schiff's reference to the CBS report, in which an unnamed Trump source claimed Trump told senators "your head would be on a pike" if they voted against him in the trial.

"Schiff believes that the only reason that we act the way that we do is because the president's going to put our head on a pike," Lankford said. "He's invalidating all of our motives. He's saying, 'You're going to ignore all the facts, and you're only doing this because we're afraid of the president, rather than we will actually be fair in the process and actually look at the facts.'"

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On Sunday, Trump again criticized Schiff for paraphrasing the content of his July 25 phone call with Ukrainian President Volodymyr Zelensky, something he has railed against since September and which his legal team referenced when it opened its defense in the Senate impeachment trial on Saturday.

"Shifty is now exposed for illegally making up my phone call, & more!" Trump tweeted.

He also criticized "Meet the Press" host Todd, wondering why he would have Schiff on after "having been exposed as a fraud and corrupt."

Trump accused Todd of conducting a "softball interview with conman Adam Schiff." He criticized him for "never even calling Shifty out on his fraudulent statement to Congress, where he made up ALL of the words of my conversation with the Ukrainian President."

Todd did ask Schiff if he regretted paraphrasing Trump's conversation. Schiff said he did not, before turning to a defense of his previous comments implying there had been evidence of collusion in 2016 between the Trump campaign and the Russian government, which was also cited by Trump's lawyers as evidence that Schiff lacked credibility.