As the historic impeachment vote played out in Washington last week, Donald Trump stood in front of a raucous audience at a rally in Battle Creek, Michigan, and relayed an anecdote from the 2016 election day that fired up the baying crowd.

He and Hillary Clinton had each rolled into the crucial swing state for their final campaign stops hours before the first ballots were cast. Clinton drew a measly audience of “500 people” to her prime-time rally, according to the president’s version of events. Conversely, he drew 32,000 supporters to a Grand Rapids arena despite not taking the stage until 1am.

“I’ll never forget that night,” he boasted. “We did it. And we won Michigan. And word is we’re much higher in the polls in Michigan than we ever were in 2016.”

The tale is not true. Trump’s rally drew a crowd of 4,200, while Clinton’s notched up 4,600. But the story was red meat to his Michigan audience last week who cheered Trump’s fantasy memory as if it presaged another victory in this key battleground state in 2020.

However, the current reality in Michigan for the now impeached president is a bit different. Polls consistently show Trump trailing top Democratic candidates in Michigan, which he won in 2016 by a mere 12,000 votes. Meanwhile, his approval numbers have remained underwater.

There are few scenarios in which a candidate can win the White House without taking this rust belt state next year, and Democrat operatives here hope Trump’s impeachment would further bolster the party, motivate the base, and sway independents. But the actual impact of the historic impeachment vote is hard to predict. Many voters across Michigan’s political spectrum questioned whether impeachment had delivered the intended results. Some even predict it will help Trump in 2020.

A supporter raises their hands in a heart gesture as Donald Trump speaks during a rally in Battle Creek, Michigan, on 18 December. Photograph: Jeff Kowalsky/AFP via Getty Images

“Did Democrats do the right thing? Oh yeah. For sure. Is it going to help them win an election? I’m not so sure about that,” said Tom Martin, a Democrat from the Detroit suburb of Warren. “It just seems like another fight, and how many more of those will there be? And how many other things are there to think about?”

Nationally, voters are split on the question of impeachment and removal from office, while a consistent majority has said Trump committed an impeachable offense. In Michigan, the reality is less clear.

Charlie Smith, a Republican who was shopping for Christmas gifts on Thursday at a mall in Macomb, said he saw a split among conservatives and liberals on the issue. Impeachment might sway some “uninformed” independents, he said, but he also called Trump a “driving force in the economy”.

“The overall factor when it comes down to voting is, ‘Hey, how am I doing economically?’ Everything is going well right now. He’s doing well by the country,” Smith added.

Macomb county, just outside Detroit, is under close scrutiny as it is one of several dozen critical swing counties nationwide in which Barack Obama won a majority before voters then switched sides to help deliver the 2016 election to Trump. Just as it’s difficult to win the general election without taking Michigan, it’s hard to win Michigan without securing Macomb.

There are doubts that impeachment moved the needle for the Democrats there.

“I find it a little hard to believe that Democrats got anything out of it,” said Bill Belanger, a state political analyst. “For people who turned from Obama to Trump, maybe there’s some disillusionment with him. But they already have a lot of other good reasons to be disillusioned.”

The impeachment inquiry could backfire in that it’s also feeding the president’s base, said Trump supporter and Macomb resident Archie Atkinson.

“It’s going to motivate me, and people in my circle have all said we’re going to get Trump back in,” he said. “Impeachment is a lot of it.”

That’s consistent with the mood at Trump’s Wednesday rally, where an estimated 10,000 fervent supporters took part in what was an upbeat celebration of their candidate on a night when their president became only the third in US history to be impeached.

We’re on the other end of the vote, and some people think that it’s a joke because Trump doesn’t care Darryl Jordan

Trump spent his two-hour Battle Creek speech shrugging off the impeachment vote by taunting, mocking and insulting Democrats and his political enemies. That sort of strategy has been effective because it undermines the situation’s gravity, said Detroit resident Darryl Jordan.

Some in Detroit, an economically struggling city of about 700,000, “turn on the TV and just see Donald Trump and his constituency trash talking, and that’s entertaining to people”, he said.

“A lot of people think that stuff is funny, and while it made sense for the Democrats to go through with impeachment, we’re on the other end of the vote, and some people think that it’s a joke because Trump doesn’t care,” Jordan added.

Convincing Detroit voters otherwise is essential to Democrats if they want to retake Michigan in 2020. Voter turnout in the city, which is about 80% black, dropped from 335,000 to 247,000 between 2008 and 2016. About 95% of those votes were cast for Democrats.

Some say the key to motivating Detroiters is offering solutions to the city’s deep economic problems, but Jordan also stressed that they need to understand that Trump’s insults and taunts are just a distraction.

“Trump is doing stuff policy-wise that’s setting us back decades,” he said. “We have to do the work to let people know that this is serious business.”