House Judiciary Committee Chairman Jerrold Nadler on Sunday said Democrats will do whatever it takes to reveal the results of special counsel Robert Mueller’s probe and will request documents from dozens of people close to the White House this week, though he downplayed talk of impeaching President Trump.

“We do not now have the evidence all sorted out to do an impeachment,” Mr. Nadler, of New York, told ABC’s This Week. “Before you impeach somebody, you have to persuade the American people that it ought to happen.”

He said Congress also has an obligation to convince Trump supporters they aren’t trying to overturn the last election — something host George Stephanopoulos called a “high bar.”

“Yeah, it is a high bar,” Mr. Nadler said. “We may or may not get there.”

The chairman said Democrats on Monday will request documents from 60 people, including Donald Trump Jr. and Trump Organization chief financial officer Allan Weisselberg, as part of investigations into what Mr. Nadler called obstruction of justice, corruption and abuse of power.

And the chairman thinks the public and Congress deserve to see what the special counsel uncovers in terms of Russian meddling in the 2016 campaign, so he will subpoena that information if the Justice Department keeps it under wraps.

“We do want the underlying evidence,” he said. “The American people are entitled to know.”

House Minority Leader Kevin McCarthy said Democrats are on a fishing expedition and, despite Mr. Nadler’s claims, will latch onto whatever they can to impeach the president.

“There’s no collusion, so they want to build something else,” Mr. McCarthy said.

Mr. Nadler said his side is conducting due diligence after Mr. Trump’s former attorney and “fixer,” Michael Cohen, used high-profile testimony to implicate the president in crimes, including pay-offs to a porn actress Stormy Daniels on the cusp of the election to cover up an alleged affair.

“Seeking to sabotage a fair election would be an impeachable offense,” Mr. Nadler told ABC. “We’ll see about that, but we’re far from making decisions about that.”

Mr. McCarthy said Mr. Cohen, as an attorney, had a responsibility to advise Mr. Trump on the law and that any violations would not be impeachable.

“Those are fines,” Mr. McCarthy said.