Republican presidential nominee Donald Trump is overhauling his struggling campaign amid sliding poll numbers. (Reuters)

For some time now, it’s been a running joke among political junkies that there might not be enough blue collar white men in America to elect Donald Trump president. The basic idea has been to mock Trump’s apparent calculation that he can sail into the White House simply by unleashing the power of backlash among this constituency with his chest-thumping ethno-nationalism.

But now it turns out that this might literally be true. Based on how this campaign has gone so far, there really might not be enough blue collar white men in America to elect Trump president, even if all of them come out to vote.

That’s the actual finding of a new analysis conducted by demographer William Frey of the Brookings Institution.

Jeremy Peters has a fascinating piece today in the New York Times that takes stock of Trump’s under-performance among a constituency that is absolutely central to his hopes of winning: White men. Peters concludes that a number of recent polls suggest that among white men, Trump is either running even with or below the margins that Mitt Romney racked up in 2012.

Given that Trump is alienating nonwhites and women to an untold degree, Trump is under even more pressure to do well among white men. Yet when it comes to that constituency, Peters notes, Trump is “showing surprising signs of weakness that could foreclose his only remaining path to victory in November.” Part of the problem for Trump in this regard is a dynamic we’ve discussed in this space: Trump is also alienating college educated whites — men included — which is one reason why he’s falling short among white men overall. That puts more pressure still on him to run up the score among non-college white men, which he and his new campaign chief, Stephen Bannon, appear to be hoping to do, judging by the new, scorched earth nationalist strategy they are planning.

Buried in the Times piece is a calculation by demographer Frey that runs as follows:

William H. Frey, a demographics expert with the Brookings Institution, a nonpartisan think tank, conducted several simulations that tried to determine how much the turnout among white men without college educations would have to increase for Mr. Trump to win. He used the most recent ABC News/Washington Post poll of registered voters that had Mrs. Clinton beating Mr. Trump in a nationwide two-way race, 50 percent to 42 percent. It was among the better polls for Mr. Trump lately.

Mr. Frey tested different turnout assumptions, including improbably optimistic ones, like if 99 percent of white, non-college-educated men turned out to vote. None of the chain of events produced a Trump victory.

In fact, even if virtually all of the white, non-college-educated men eligible to vote did so, Mr. Frey found, Mrs. Clinton would still win the popular vote by 1.1 million.

In other words, assuming the spreads in the recent Post/ABC poll hold, if pretty much every single blue collar white male in America turns out to vote on Election Day, Trump would still fall well short of winning.

The Post/ABC poll found that Trump is dominating among non-college whites (58-33) and particularly among non-college white men (67-25). But that’s offset by Clinton’s advantage among college educated whites, and the fact that she keeps it closer among non-college white women than this spread was in 2012.

I checked in with Frey for some more information about his simulation. He told me that he had assumed that 2012 level turnout levels (based on census data) would remain constant among all other voter groups in 2016 — using eligible voting-age adults — and only inflated turnout among non-college white men, to 99 percent. Under that scenario, Trump still loses, mainly because he’s getting swamped among other voter groups, and is losing among college educated whites.

“If the voting on election day is in line with the Washington Post poll, even if all non-college white men show up on Election Day to vote, it would be difficult for Trump to win,” Frey told me.

To make this worse for Trump, Frey added, it is far-fetched to begin with to assume that non-college white men will turn out at larger rates than college-educated whites overall will. The opposite is more likely to be the case, Frey said.

“And this doesn’t even play around with the possibility that college educated white women may turn out in larger numbers than usual in this election,” Frey added. That obviously could happen with a woman as the Democratic nominee.

Of course, the voting on election day may not look like the Post poll at all. The spread may well tighten in coming weeks, particularly if Trump takes steps to broaden his appeal with all these other voter groups. Still, he shows no signs of doing that. Indeed, as I argued this morning, all signs are he’s doing the opposite.

“With almost two-thirds of voters holding an unfavorable view of Trump, it’s not clear how many more people he can rally to his side without a big change in tone and message,” Nate Silver wrote today. “But Trump and his acolytes seem to be in profound denial about the narrowness of their appeal.”

And so, if current trends continue, it may really end up being true: There may not be enough blue collar white men in America to elect Trump president. Even if all of them come out to vote.