When Republican Ben Sasse was elected in an upset win two years ago, few would have predicted he would become the public face of an underground movement to oust his party's standard-bearer for the presidency.

But that's the unenviable position the Nebraska senator has found himself in, as one of just two elected Republicans to openly refuse to back Donald Trump in his bid for the White House. "I can't support someone that I don't think would take the oath of office in good faith," Senator Sasse told the Washington Post .

Sasse openly shares his disgust with Trump on Twitter and with reporters, but behind closed doors the #nevertrump movement is swelling in support to replace the billionaire with a more palatable candidate.

It's now five weeks since Trump all but clinched the nomination and, publicly at least, the major Republican powerbrokers have all fallen into line behind the man who would stop Hillary Clinton becoming president.

But a series of missteps have seen Trump's popularity plunge to the lowest level of any major presidential candidate in recent history, a fact he himself has been forced to confront by firing his campaign manager yesterday.

It is near-impossible to give Trump the boot at the looming Republican National Convention (RNC) in July, where Trump’s candidacy will be officially confirmed.

In spite of this, the #nevertrump camp is garnering support.

Operatives behind the scenes are reportedly searching for loopholes to allow Trump's delegates to defect and support another candidate.

The belief among the Republican establishment is a coup overturning the will of primary voters would be less damaging to the party than a Trump nomination.

Speculation of an intra-party coup has only intensified with the appointment of two Mitt Romney -aligned Republicans to the RNC Rules Committee.

Romney has been among the most fervent critics of Trump and has been part of the group searching for an alternative candidate.

Even Republican Speaker Paul Ryan refused to dismiss the possibility of a party revolt.

"The last thing I am going to do is weigh in and tell delegates what to do," he told Meet The Press on Sunday.

"The last thing I would do is tell anybody to do something that’s contrary to their conscience."

But Trump himself has hosed down the #nevertrump speculation.

"Who are they gonna pick? I beat everybody," Trump said in Las Vegas on Saturday.

"And I don’t mean beat—I beat the hell out of them."

Trump raises a substantial problem for the #nevertrump movement. A rival conservative would alienate Trump's loyal followers but would probably not pick up enough Clinton supporters to win. And nobody wants to run a race they'd almost definitely lose.

The other problem is even bigger. Even if the delegates bound to Trump could defect, it's unlikely many of them would. In most states those delegates were handpicked by the Trump campaign, and they are composed of some of his most loyal followers.

In reality, the #nevertrump movement is one based among the Republican party elite, and mostly behind closed doors.

Trump can do without the Republican establishment's public support. Where it is hurting him most is in the back pocket.

Trump's campaign has just $1.3 million in the bank this month, compared with Hillary Clinton 's $42 million. Despite his pledges to bankroll his own presidential run, Trump has been sparing with his own donations. In May, Clinton raised nine times as much money as Trump did, even while running a primary against Bernie Sanders.

With a disenchanted electorate, building up a cash advantage to spend on advertising and campaign infrastructure is crucial.