On a damp and windy day, members of the United Auto Workers (UAW) picketed outside a sprawling Ford plant in Wayne, Michigan, burning logs in barrels for warmth.

The plant makes the Ford Bronco, and workers there were among the first to strike when union contract negotiations between the UAW and the car companies collapsed earlier this month.

Strikers wearing red shirts and carrying signs chanted: “What do we want? Contract! When do we want it? Now!” and “No pay no parts,” as drivers passing by on the busy highway blared their horns in support.

The UAW strike has pushed into its third week, and unlike many strikes, it has managed to stay in the news – not least because on Tuesday, Joe Biden became the first US president to join strikers on a picket line in what feels like the unofficial kick-off to the 2024 campaign season.

“Stick with it. You deserve a significant raise,” Biden told the crowd in a minute-long speech. “We saved them [the car companies]. It’s about time they step up for us.”

The speech may have been short and sweet but the reaction was overwhelmingly positive.

Walking the picket line, Larry Hearn, a 61-year-old UAW committee member, said: “We’re out here on the frontline taking the brunt for everybody, losing money. The support feels good. We don’t need him to get in our business and secure us a contract, but his support is enough. It hits home with people.”

The Donald Trump campaign called Biden’s visit to the picket line a “cheap photo op”, but at least some workers disagree with that assessment.

“It’s about time a president stood up for workers instead of the billionaire class and donor class,” said Quintin Tucker, 57, who works in the plant’s final assembly department.

Trump will visit a non-union auto shop tomorrow, a fact that was not lost on those outside the Wayne plant.

“That’s where his loyalties lie,” Walter Robinson, a 57-year-old quality inspector, said. “If he wants to be with working people who are struggling, then he would be here. I don’t know who he is playing for – is he playing for working people, or corporations?”

“He has to go to a non-union plant because if he came here, we wouldn’t let him in,” added Hearn. “If he pulled up in his motherfuckin’ motorcade right now, we would not let him in.”

But it’s too early to count Trump out, said Robinson. The former US president did beat Hillary Clinton in the state in the 2016 election and still has his fans.

Trump gets a lot of support among union members because of “guns, gays and taxes”, Robinson said, and inflation has not helped Biden.

“That resonates with a certain sector of people,” he added, estimating that there is about a 60-40 split at the plant in support for Biden and Trump respectively.

Hearn said he is a Democrat and that most union members will say they are, but added, “You never know what someone is going to do when they get behind the booth.”

Frank Wells, a 27-year plant veteran, is a Democrat who is not impressed by Trump, especially because he is visiting a non-union shop.

“Let’s be real. He doesn’t support what we’re doing. He’s corporate. He’s a billionaire, a businessman, but we’re out here fighting for our lives,” Wells said.

Tucker estimates support for Biden and Trump in the plant is closer to 50-50, and that Trump draws support for his “cult of personality” and effective use of social wedge issues.

Trump does not really support the UAW, Tucker said, because “he is from the billionaire class and it’s against his interest”. Still, he added: “People vote against their economic interest in favor of cultural issues.”

He scoffed at Trump’s planned visit to a non-union shop. “The anger that we’re feeling right now – he doesn’t want that to rub off on him so he went somewhere safe, where they don’t have any skin in the game.”