Rep. Adam Schiff, the Democrat who is expected to lead the House Intelligence Committee next month, said President Donald Trump could "be the first president in quite some time to face the real prospect of jail time."

"There's a very real prospect that on the day Donald Trump leaves office the Justice Department may indict him," the California lawmaker said Sunday on CBS' "Face the Nation" when asked about a Friday court filing by federal prosecutors that appeared to link Trump to a campaign finance violation.

While there has been a lot of speculation in the news media about potential presidential pardons for people convicted of crimes as a result of special counsel Robert Mueller's Russia probe, Schiff said the bigger question may come when "the next president has to determine whether to pardon Donald Trump."

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Prosecutors from the Southern District of New York appeared to implicate Trump in one of the felonies committed by his former personal attorney, Michael Cohen.

Cohen pleaded guilty to violating campaign finance laws when he made hush payments before the 2016 election to two women alleging past sexual encounters with Trump. According to prosecutors, Cohen carried out the payments "in coordination with and at the direction" of Trump.

"The prosecutors in New York make a powerful case against" a future pardon for Trump, Schiff said. Such a pardon would send the message that "while people are out walking precincts and doing what they should do in campaigns, the rich and powerful seem to live by a different set of rules," he said.

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But Schiff said "I think we need to wait until we see the full picture" before declaring that the president should be impeached. After Cohen's allegation, Schiff said the question becomes: "Is a crime directed and coordinated by the president which helped him obtain office sufficient to warrant his removal from that office?"

He said it would first be necessary to see the full "quality of the truth" behind the allegation. "But I think we also need to see this as part of a broader pattern of potential misconduct by the president and it's that broad pattern I think that will lead us to a conclusion about whether it rises to the level to warrant removal from office," Schiff said.

Rep. Jerry Nadler, D-N.Y., said Friday's court filings "show that the president was the center of a massive fraud."

Nadler – who will likely be the next chairman of the House Judiciary Committee – told CNN's "State of the Union" host Jake Tapper on Sunday that the campaign finance violation alleged by Cohen would be "impeachable offenses."

But "whether they are important enough to justify an impeachment is a different question," Nadler added.

"You don't necessarily launch an impeachment against the president because he committed an impeachable offense," Nadler explained. "An impeachment is an attempt to, in effect, overturn or change the result of the last election. And you should do it only for very serious situations."

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