In the handful of more rural, conservative-leaning districts where the party has a better shot of winning, the message is blunter.

In Minnesota, ads from groups like the Congressional Leadership Fund and the National Republican Congressional Committee try to link Mr. Hagedorn’s opponent, Dan Feehan, to people and themes that conservatives have portrayed as a threat, like Mr. Soros, the liberal philanthropist who has been smeared with anti-Semitic attacks; Mr. Kaepernick, the black football player famous for kneeling during the national anthem; and now the migrant caravan.

In one, a doctored image appears to show Mr. Feehan, an Army veteran, saluting Mr. Kaepernick. Another shows Mr. Kaepernick alongside two other favorite villains of conservatives — Nancy Pelosi, the House Democratic leader, and Keith Ellison, the Minnesota congressman who is black and Muslim and is now facing abuse allegations as he runs for state attorney general. Mr. Feehan’s face appears on the screen, and the announcer intones, “He’s one of them.”

Ads like these have aired repeatedly across the district’s 12,000 square miles of farmland and small towns, making it what Republicans say is the most active political laboratory for the bald appeals to white racial and cultural anxieties that President Trump and many Republicans are using to drive conservatives to the polls.

The First District, which is 90 percent white, fits the demographic profile of many of the places where Mr. Trump has been confined to campaigning by Republicans who do not want him in more diverse districts. Given Mr. Trump’s self-described “nationalist” views, some Republicans believe their path to staying in power in the Trump era is increasingly narrow and heavily dependent on the parts of the country that are the most white and rural.

Jason Hulburt, a production line supervisor from Albert Lea, said he planned to vote for Mr. Hagedorn on Tuesday, a choice he made in part because of how important he thinks it is for Mr. Trump to have like-minded Republicans in Congress.

“Donald Trump knows what he wants, and the Democrats are afraid of the issues Trump talks about,” he said Friday night as he finished a brandy and water at Eddie’s, a local bar. “They’re afraid to offend certain people. Trump is not afraid.”