BIRCH RUN, Mich. — After Ted Cruz and Donald Trump dominated Saturday’s three Republican caucuses and lone primary, both the Marco Rubio and John Kasich campaigns put out “we-ain’t-down-yet” statements suggesting that the GOP race would not be decided until the Cleveland Convention.

As John Weaver, Kasich’s top strategist, put it in a memo to the media, “No candidate is currently on track to win the nomination outright. … Governor Kasich is the candidate best positioned to arrive in Cleveland and exit as the nominee.”

The current delegate math (Trump has around 45 percent without counting uncommitted delegates) argues for Chaos in Cleveland. Saturday’s results — plus talking to local Republicans at a party dinner — suggest that Trump may be paying an electoral price for the swaggering vulgarity of his last debate performance.

The unifying battle cry of the anti-Trump Republicans, from an energized Mitt Romney on down, has become, “Let the Convention Decide.” It is a strategy that I have endorsed as a columnist seeing Trump as “the embodiment of the authoritarian temptation.”

What I didn’t calculate, though, was how wedded rank-and-file Republicans are to voter sovereignty in the primaries. Conventions are now viewed as TV backdrops – not decision-making bodies. That, at least, was the overwhelming reaction Saturday night at the Saginaw County Republican Party’s Lincoln Day Gala.

“I think if someone’s winning by the rules set out, he should be the nominee,” said Saginaw state Rep. Tim Kelly in a welcoming address to the dinner. “We’re a party of rules, we’re a party of laws. Otherwise, we would just play into the narrative of the left that the system is rigged.”

Kelly, who voted for Cruz by absentee ballot, added in an interview, “I think it was wrong for Mitt Romney to do what he did the other day by pulling the fire alarm one-third of the way through the primaries.” (In the GOP 2012 primary, Romney narrowly edged Rick Santorum in Saginaw County, which is north of Flint).

The roughly 250 Republicans, almost all over the age of 35, at the Saginaw County dinner are the backbone of the party. They are the small-town Republican establishment — the traditional Rotary Club and Chamber of Commerce types who worry about recruiting county commissioner candidates.

Party activist Herb Hansen, a retiree from Saginaw Township, regards Trump as a fraud: “His ‘Make America Great Again’ sounds the same — it’s meaningless — as Obama’s ‘Hope and Change.’” But Hansen, who strongly backs Kasich, has no stomach for a convention fight, saying, “Whatever the rules are, follow the rules and don’t conspire to circumvent the rules.”

Hansen was wearing a button from the 1909 centennial of Abe Lincoln’s birth. I didn’t have the heart to remind Hansen that Honest Abe was nominated through backroom deals in Chicago in 1860.

Kasich, who addressed the Saginaw County dinner Saturday night, did not talk explicitly about a contested convention. But it was implicit in his stump speech as he suggested that he alone could bridge the fractures in the GOP: “I understand Donald Trump. It’s not that I understand him. But I understand the people who are for him.”

Kasich’s problem — like Rubio’s — is that he lacks a plausible path to a majority before the convention. So in Tuesday’s Michigan primary and afterwards, the Ohio governor faces a two-pronged problem: convincing Republicans to vote for him and later getting them to accept the verdict of a contentious contested convention.

From the vantage point of Washington or New York, it is easy to see the rise of Trump — the bilious billionaire with no ideological core — as a hostile takeover of the Republican Party. But people like Pat Wurtzel, a Saginaw County commissioner, refuse to view things that way.

Wurtzel attended last Thursday’s Detroit debate with a ticket provided by the Rubio campaign. “I was embarrassed at the rudeness of the crowd,” he said. “I was embarrassed to be a Republican at the debate.”

But even though Rubio ridicules Trump as a “con artist,” Wurtzel would happily accede to a Trump triumph in the primaries or even a lead heading to Cleveland. As he put it, “The people who are electing the president are wise enough to make the right decision.”

I reminded Wurtzel — to no avail — that Ronald Reagan refused to concede anything in his uphill 1976 battle against incumbent President Jerry Ford. “At the end of the primaries,” Elaine Kamarck writes in Primary Politics, “[Reagan] was only 117 votes behind Ford, and there was enough uncertainty about the delegate count that, for all practical purposes, the two candidates were tied as they went into the convention.”

But Republicans were apparently made of sterner stuff back in 1976. Today a trailing candidate like Reagan would be ridiculed by the media for not dropping out and viciously attacked by fellow Republicans for destroying party unity. In the four decades since 1976, we have lost any collective memory of the kind of brokered conventions that gave the nation Dwight Eisenhower and John Kennedy.

Republicans are still three months away from the end of the major primaries with California and New Jersey on June 7. Trump’s delegate lead (knock wood) may have faded by then — or mainstream Republicans in places like Saginaw County may have become alarmed at the prospect of the bumptious self-promoter at the top of the ticket.

But at the moment, anyway, there is a limited appetite for using scorched-earth tactics against Trump in Cleveland. And those who concoct anti-Trump scenarios (myself included) have to take that rank-and-file resistance into account.

Roll Call columnist Walter Shapiro is covering his 10th presidential race. A fellow at the Brennan Center at NYU, he is lecturer in political science at Yale and is the author of the forthcoming in June ‘Hustling Hitler: The Jewish Vaudevillian Who Fooled the Fuhrer.’ Follow him on Twitter at @MrWalterShapiro.

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