DAYTON, Ohio — At Slyder’s Tavern, Matt Kazee, a machinist, drank a couple of beers as he waited for burgers to take home for dinner. His tab was about equal to the increase in his take-home pay after President Trump’s tax cut found its way into the nation’s paychecks.

“I have seen a little uptick in my paycheck, about what I expected, about 30 bucks,” said Mr. Kazee, who voted for President Barack Obama in 2008 before backing Mr. Trump in the 2016 election. “It felt to me about like where things were 15 years ago.”

His underwhelmed reaction was not what Republicans had in mind. The white working-class voters in the industrial Midwest who helped put Mr. Trump in the White House are now seeing the extra cash from the tax cut, the president’s signature domestic policy achievement and the foundation for Republican election hopes in November.

But the result has hardly been a windfall, economically or politically. Other workers described their increase as enough for a week’s worth of gas or a couple of gallons of milk, with an additional $40 in a paycheck every two weeks on the high side to $2 a week on the low. Few are complaining, but the working class here is not feeling flush with newfound wealth.