More than 50 congressional Democrats reportedly back impeachment proceedings against Donald Trump. But on Sunday morning, senior figures highlighted the split that remains between those demanding swift action and their party leaders.

Adam Schiff, the House intelligence committee chair, was asked if he and House speaker Nancy Pelosi could “hold the line” against mounting calls for impeachment.

“We’re going to do what’s right for the country,” Schiff told ABC’s This Week, “and at this point, the speaker has not reached the conclusion – and I haven’t either – it’s best for the country to put us through an impeachment proceeding that we know is destined for failure in the [Republican-held] Senate.

“Now, that calculus may change if the president continues to stonewall [against congressional oversight], if the president continues to demonstrate his unfitness for office. There may be little additional cost to going through that process.”

I think if it is a close call, close calls go against putting the country through that Adam Schiff

Calls for impeachment have intensified in the wake of a press conference on Wednesday in which Robert Mueller undermined Trump and his allies’ claims of exoneration over Russian election interference, links between Trump and Moscow and the obstruction of justice.

“If we had confidence that the president clearly did not commit a crime,” Mueller said, “we would have said that”.

Pelosi has said publicly that Trump appears to be “goading” Democrats toward impeachment, thinking it will ramp up support from his base. But she has also called impeachment a “fool’s errand” and maintained: “You don’t bring an impeachment unless you have all the facts.”

The speaker is reported to have said privately that it would be imprudent to impeach as the 2020 election approaches.

Schiff conceded that impeachment proceedings would be, “in a way … the ultimate form of censure in the House”.

“But we’re not there yet,” he said, “and I think if it is a close call, close calls go against putting the country through that.

“We have an important legislative agenda to try to advance, we have important oversight work we can do outside the context of impeachment, and I think at this point that is still the preferred course.”

Schiff also slammed the Republican party, saying it has “turned itself into a cult of the president’s personality” that is unlikely to abide by its constitutional duties.

House majority whip James Clyburn told CNN’s State of the Union Congress “has to determine the timing for impeachment”.

We think that we have to bring the public along James Clyburn

“What Nancy Pelosi is trying to do, and the rest of us in the House of Representatives, is to develop a process by which we can efficiently move on this issue, so that, when we get to a vote, it would be something that she calls ironclad, I call effective,” he said.

Asked if House Democrats were waiting for signs of support from the public or among Senate Republicans, he said: “We think that we have to bring the public along.”

Democrats “aren’t waiting on the Senate”, Clyburn said, although he suggested that properly executed House proceedings might prompt the Senate to act.

Asked if he thought Trump would be impeached, just not right now, Clyburn said: “Yes, [that’s] exactly what I feel.

“I think we have already begun. We have got all of these committees doing their work. We’re having hearings. We have already won two court cases. And there are other cases that are still to be determined.

“So, why should we get out in front of this process? Why don’t we just continue to go along? And … right now, we are winning this issue.”

The New Jersey senator Cory Booker, a contender for the Democratic presidential nomination, was asked on CNN why he voiced full support of impeachment for the first time after Mueller spoke.

“Well, it was a few weeks of seeing a president who wants to undermine …constitutional intent, and say that he’s above the law,” Booker said.

“He has not been complying with subpoenas. He has not been complying with legitimate congressional inquiries to continue the investigation that Mueller, very specifically, said it’s on Congress now to continue after he put this report forward that clearly indicated that there is potential corruption and obstruction of justice.

“This president is not above the law. He should not be able to stop the checks and balances on the executive. And I feel like we have a moral obligation now to investigate this president.”