A movement of rogue electors convinced that Donald Trump is unfit for the Oval Office has a last chance to block him on Monday.

If at least 37 conscientious members of the U.S. electoral college refuse to toe the line by voting with their state's popular vote, their hope — and it's indeed slim — is that they'll deny Trump the presidency.

Here's how.

The Hamilton Electors

Democratic presidential elector Bret Chiafalo stands outside the U.S. Courthouse before a hearing in Seattle. Chiafalo is one of two Democratic presidential electors from Washington who wants to see Donald Trump denied the presidency. (Elaine Thompson/Associated Press)

Dissenters calling themselves the Hamilton Electors are relying on what the movement's co-founder Bret Chiafalo has called a Hail Mary play, a tiebreaker that goes to the House of Representatives.

Chiafalo, a Democratic elector from Everett, Wash., banks on this happening if Trump falls short of winning a majority — or 270 votes — in the 538-member electoral college.

The number of Hamilton Electors varies depending on reports. Harvard Law professor Larry Lessig, who has offered pro-bono legal support to electors who risk punishment by defecting from Trump, has reportedly said "at least 20" Republicans are considering doing so.

(Lessig, who argues electors are free agents with the right to vote their conscience, has not provided evidence of the 20 electors.)

37 is the new magic number

Ohio governor John Kasich, left, and 2012 Republican presidential candidate Mitt Romney have been floated by would-be rogue electors as consensus Republican alternatives to Trump. (Matt Sullivan/Reuters)

First, a reminder: Trump crossed the majority threshold with 306 electors pledged to him on election night.

But the Hamilton Electors point out those were merely pledged votes. Anything might change at the ballots on Monday. If Chiafalo gets his way, "nobody gets 270 electoral votes," meaning that "the emergency brake" gets yanked.

The Hamilton Electors would be happy with a draw. Denying Trump a majority would kick the choice of the next president over to Congress. The House would then consider the top three electoral vote-getters: Trump, Democratic contender Hillary Clinton, and "somebody else," Chiafalo says.

The defectors will need to persuade enough electors — in this case 37 — to flip votes away from Trump.

This isn't about electing Clinton

Democrat Hillary Clinton, who ran against Trump in the 2016 election, speaks on Capitol Hill. (Evan Vucci/Associated Press)

Rather, it's about not electing Trump. The Hamilton Electors are advocating for a "consensus" or "compromise" Republican.

"Someone like John Kasich or Mitt Romney," says Chiafalo, who supported Bernie Sanders in the Democratic primary. "Even if I disagree with his policies, at least he's not an existential threat like Trump."

Clinton won Chiafalo 's home state of Washington, so he would by tradition cast his electoral vote for her. But the 38-year-old network engineer sees no viable path for Clinton to get the presidency, noting it's unlikely Republican electors "would vote for someone their party generally hates."

"If uniting against Trump means convincing Republican electors, the answer has to be a Republican."

So far, only one Republican elector, Christopher Suprun of Texas, has publicly stated, in a New York Times op-ed, that he won't vote for Trump because he is "not qualified for the office."

What's driving these rogue electors

A statue of Alexander Hamilton stands in New York's Central Park. A group of Hamilton Electors is mounting a last-ditch effort to stop Donald Trump from becoming president. (Mike Segar/Reuters)

They believe Trump is unqualified. It's a primary reason they say deserting him would be justified, citing a framework for the electoral college written by Founding Father Alexander Hamilton.

That 1788 constitutional essay states that there should be a "moral certainty that the office of president will never fall to the lot of any man who is not in an eminent degree endowed with the requisite qualifications."

The Hamilton Electors movement is named after Hamilton, who authored Federalist No. 68, part of a package of 85 essays arguing for the ratification of the U.S. Constitution.

Constitutional historian Andrew Rudalevige calls it "a good guide to the founders' intentions." For the Hamilton Electors, it demonstrates that the electoral college was designed to keep someone like Trump from taking the nation's highest office.

Foreign influence

The CIA suspects Russian hackers meddled in the U.S. presidential election in an effort to get Trump elected. Analysts say directives for such action would have come from leaders such as President Vladimir Putin. (Sergei Karpukhin/Pool/Associated Press)

Current events are renewing interest in Hamilton's original text, says Rudalevige, who teaches at Bowdoin College in Maine. Take, for example, revelations that the CIA suspects Russian hackers meddled with the election to try to tip the outcome toward Trump.

Hamilton's article expresses concern about a president who could be under the influence of foreign powers, warning against efforts of "foreign powers to gain an improper ascendant in our councils" to elect "a creature of their own."

"The argument with the Russian hacking thing is: Could that be a foreign power interfering in our election to install their own candidate?" Rudavelige says. "And then you have to pair that with the 'Trump is unqualified' trope."

Another section of Hamilton's essay is leery about the possibility of Americans electing a demagogue, or someone with "talents for low intrigue, and the little arts of popularity." Trump's opponents say his rabble-rousing, populist appeal and flirtation with white nationalist sentiment is evidence of demagoguery.

Still a long shot

The U.S. House of Representatives meets in October 2015. If 37 Republican electors ignore their obligations to vote for Trump, the Republican-controlled House may decide the next president. (Gary Cameron/Reuters)

Stopping Trump remains feasible in the sense electors can vote for whomever they want, Rudavelige says.

"But it's unfeasible in the sense electors are chosen for that job by virtue of them being party loyalists unlikely to show exactly this kind of independence."

Even if the required 37 Republican electors spurn Trump and the presidential decision-making passes to Congress, there's no guarantee the Republican-led House of Representatives wouldn't just follow the will of the party and go for Trump anyway.

Nor is there any guarantee Kasich or Romney would even take the job.

"You'd be asking [Congress] to put somebody into the Oval Office who's not on the ballot," Rudavelige says. "It's a tricky situation of democratic accountability."

Some setbacks

While campaigning for president, Trump dismissed claims by Hillary Clinton's campaign that Russia was trying to help him by leaking thousands of emails from the Democratic National Committee. (Carlo Allegri/Reuters)

Last week a Colorado judge rejected a lawsuit to try to overturn the state law binding electors to vote for the winner of their state's popular vote. There are 28 states with similar laws.

Non-conformers might face jail time or fines, depending on their state.

Chiafalo is undeterred, though he could be subjected to a $1,000 fine. He and another Washington elector sought an injunction against their state's law, which was rejected. They plan to file an appeal.

Meanwhile, the Clinton team is making an appeal for electors to be shown information about the suspected Russian hacking before they cast their votes.

How many voters, if any, stray from convention on Monday won't be officially known until the electoral college results are certified in Congress on Jan. 6.