Representative Greg Landsman’s pitch to the voters of his politically competitive district in Ohio goes something like this: You may once have preferred Republicans, but the leaders of today’s G.O.P. have gotten, well, too weird.

Vote instead, he argues, for someone who is “normal.”

It is a message Mr. Landsman, a Democrat, delivered recently to a gathering of moderate donors in a penthouse in downtown Cincinnati, drawing laughter. It appeared to land equally well at a predominately Black church, where the crowd nodded along. And at a focus group of suburban voters, a former Republican told him she knew exactly what he meant.

He is not the only one. Taking a page from Gov. Tim Walz of Minnesota, the Democratic vice-presidential nominee whose “these guys are just weird” quip about the Trump-Vance ticket caught fire on the left, Democrats in competitive congressional contests across the country are trying to make their races a contrast between the normal and the weird.

Vice President Kamala Harris highlighted the tactic on Tuesday night in her debate against former President Donald J. Trump. As he peddled the false claim that migrants were marauding through American towns eating people’s pets, a bemused-looking Ms. Harris simply laughed and shook her head at him, muttering, “Unbelievable.”

It is a sharp pivot from the days not long ago when Democrats suffused their campaigns with dark warnings of the dangers of extremism, arguing that electing Republicans was a threat to democracy itself. Now the emphasis is on a much lighter — and perhaps more broadly appealing — theme that conjures the classic political trope of which candidate you would rather have a beer with.