In a television advertisement released in September, Republicans deployed Mr. Bryce’s brother, a police officer, as a spokesman. He argued the tweet is a reason to vote for his brother’s opponent.
“When people refer to police officers as ‘terrorists,’ that hits a little too close to home,” said James Bryce, as the tweet flashed across the screen. “I don’t want to be represented by someone who has shown contempt for law enforcement.”
Mr. Trump, to big applause, alludes to Mr. Kaepernick’s protest at almost every campaign rally. During a recent stop in Minnesota 1st Congressional District, where the Democratic nominee, Dan Feehan, had previously expressed support for Mr. Kaepernick’s protests, the crowd erupted when Mr. Trump said, “We’re proud to stand for our national anthem.”
Mr. Feehan is an Iraq War veteran but in an increasingly conservative portion of the state, which stretches across Minnesota’s southern border. It is one of the few seats election experts think could flip from Democrats to Republicans this November, and Republicans see the line of attack as especially potent.
On the Democratic side, some candidates have tried to make explicit appeals to racial justice to inspire new voters. Mandela Barnes, the party’s candidate for Wisconsin lieutenant governor, donned Mr. Kaepernick’s jersey while on the campaign trail, and had a Twitter row with Gov. Scott Walker, a Republican, regarding the same issue. Representative Beto O’Rourke of Texas, trying to unseat Mr. Cruz, went viral with his speech to black audiences regarding the death of Mr. Jean, who was killed in his apartment after an off-duty police officer said she mistook him for a burglar.
Even in fights among Democrats, Ayanna Pressley, the Boston city councilor who defeated incumbent Representative Michael Capuano, used her support of Mr. Kaepernick’s protests to draw a rare point of daylight between herself and Mr. Capuano. She was battling to represent Massachusetts’ only congressional district with a majority of nonwhite voters, and some in the city believe the issue helped push Ms. Pressley over the top.