NEWARK, Ohio — His Republican opponent doesn’t say much publicly about the Trump tax cuts, but on a warm night in a small-town union hall an hour outside Columbus, Danny O’Connor was happy to talk about them — a lot.

“We just saw, this last December, a $2 trillion swipe of the national credit card, a giveaway to big corporations,” Mr. O’Connor, the Democrat in a special election on Aug. 7 for an open congressional seat here, told the crowd, drawing nods. “That doesn’t do anything for us. It doesn’t do anything for working people.”

That seems to go against what Republicans intended. Party leaders in Washington talk frequently about the tax cuts and a “Trump boom” that will doom the “blue wave” this election year — or at least shrink it to a ripple. News on Friday that the economy grew at a robust 4.1 percent between April and June seemingly supplied more ammunition to a message centered on tax cut-fueled prosperity.

But so far, that is not how it is playing out on the campaign trail.

With little more than a week to go before voters here head to the polls, the airwaves are instead dominated by more general promises to create jobs and, from Republicans, by dark warnings on wedge issues such as immigration, meant to rally the conservative base. A Republican “super PAC” is blitzing the Ohio airwaves, contending that electing Mr. O’Connor will mean “more crimes, more drugs.”