Donald Trump faces a higher risk of being removed from office than is widely assumed if senators vote on his fate by secret ballot, according to a Republican challenging him for the US presidency.

Bill Weld, the former governor of Massachusetts, is mounting a long-shot challenge to Trump in the Republican primary and he is now suggesting the president might not even be on the ballot in November 2020.

Conventional wisdom holds that, in the wake of the damning testimony of the acting ambassador to Ukraine, Bill Taylor, of a quid pro quo, House Democrats’ inquiry will inevitably result in Trump’s impeachment before the end of this year but the Republican-controlled Senate will then acquit him.

“I do think the House will send it over to the Senate for a trial,” Weld said before a recent campaign stop in New Hampshire. “I don’t really have a prediction on the Senate. I have no idea what the chances are.

“A straw in the wind was provided by former senator [Jeff] Flake of Arizona recently when he said if there was a secret ballot, there would be 30 to 35 votes to convict. Well, all you need is 20. I think from Senator Flake that was a trial balloon to plant the idea in Leader [Mitch] McConnell’s head that maybe a secret ballot would inform his judgment. If they go to a secret ballot, I think you could see some real movement.”

A secret ballot could shield some Republicans from the wrath of Trump’s fervent base ahead of primary elections. Few have been willing to speak out against Trump over the past two and a half years, although his decision to withdraw US troops from Syria, and his abortive attempt to host the next G7 summit at one of his properties, sparked rare dissent this month.

Weld, who at 74 is a year older than Trump, has been here before. Along with Hillary Clinton, a fellow aspiring lawyer at the time, he was on a bipartisan team recruited by the House judiciary committee to write a congressional memo entitled Constitutional Grounds for Presidential Impeachment during the Watergate scandal of the 1970s.

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Watergate eventually led to the resignation of former president Richard Nixon before he could be impeached.

Trump’s actions have been even more egregious, Weld argues, because they invited foreign interference in American democracy and, in his view, are tantamount to treason. “Worse than Watergate? Almost no comparison. Watergate was a single lie. Did the president know? This is a tissue of lies, to use the British expression,” he said.

But Weld does see some parallels between Trump’s predicament and Nixon’s slow then sudden downfall.

Weld said: “The one thing that strikes me most vividly is political and it’s that the president is hanging the members of his own party out to dry in forcing them to go through the draining, even exhausting effort of defending him.

My sense more broadly, being on the hustings, is everyone’s exhausted by Trump Bill Weld

“The Republicans in the Senate were defending Nixon up until the day when the tapes became public and then two days later he had 0% in the Senate. Dick Nixon had won 49 states not so long before that.”

He added: “My sense more broadly, being on the hustings, is everyone’s exhausted by Trump. They’re very tired and so they really don’t want to be forced to wallow in Trump. They’d rather think about healthcare and other issues that have more to do with their daily lives.”

Taking the oath of office in 1974, Nixon’s successor, Gerald Ford, declared: “My fellow Americans, our long national nightmare is over.” Just as it did then, the Republican party can regroup and turn over a new leaf, according to Weld, who has been joined in the primary by the former South Carolina governor Mark Sanford and ex-congressman Joe Walsh.

“First of all I think all the Republican senators who defend Mr Trump will lose next year so they’ll be very much diminished in their ranks,” he said. “Second, I think as soon as Mr Trump is gone by whatever mechanism – whether it’s election or removal – everyone’s going to say: ‘That was a bad dream. Is it safe to come out now?’ So I don’t think his influence is going to be permanent. Things can move quickly in a good direction as well as in a bad direction.”