During an appearance on NBC's "Meet the Press", Schiff was asked if he saw Trump's tweet that "he still hasn't paid the price for what he did in our country!" as a threat. Schiff replied, "I think it is meant to be". Trump's attack on Twitter in Schiff was one of several that the president launched online Sunday against Democrats and his Senate impeachment trial.
In concluding the opening argument of the House on Friday night, Schiff, a California Democrat and President of the House's Intelligence President, made a lengthy argument to remove the President from office on charges of abuse of power and obstruction of Congress .
Schiff said on Sunday that he was arguing that it would be very difficult for senators to face Trump.
"And I think I have to be very sincere about this … I argued that it will take moral courage to face this president," he said. "And this is an angry and vindictive president. I don't think there is any doubt. If you think there is, check out the president's tweets about me today, saying that I should pay a price."
On Sunday, Trump also tweeted insults at "Meet the Press" host Chuck Todd, who conducted the interview with Schiff.
"I think it was a big mistake"
Trump's legal team, he said, "basically recognized the scheme" – and that his main argument was "you don't need a fair trial here", adding that there was no "exoneration" if the country was deprived of a fair trial.
"I was surprised. I think it was a big mistake … they are bent on the same crazy conspiracy theory that Ukraine invaded the DNC server. It's surprising," said Schiff. "On the first day of the defense of the president, saying that the president should disbelieve his own intelligence agencies, he has every right to believe (Vladimir Putin, Russian president). I would not like to argue."
President Jay Sekulow's personal lawyer has signaled that the defense team is likely to go after former Vice President Joe Biden and his son Hunter Biden, in addition to Russia's investigation of the former agent's president and opposition research dossier British intelligence officer Christopher Steele.
The president's team is making its presentation, as GOP sources from the White House and the Senate told CNN that they are confident they will defeat a vote next week by more witnesses who would extend the trial. But there was no mention of the former vice president or his son on Saturday.
Schiff, asked about a possible deal in which Democrats and Republicans would call the witnesses they wished to obtain a testimony, said he believed the president "has the right to call relevant witnesses … in his defense", but made it clear he did not believe that Hunter Biden is a "relevant witness".
"If we are talking about a fair trial … (the senators) cannot say," Well, we are going to allow the president to exchange witnesses who will not shed any light on the facts, but would allow him once again to try to taint his opponent, "said Schiff.
"Hunter Biden cannot tell us anything about withholding military funding. Hunter Biden cannot tell us why the President would not leave the President if Ukraine entered the Oval office. Hunter Biden cannot tell us anything about it," he added .
CNN's Jeremy Herb, Betsy Klein and Manu Raju contributed to this report.