Mike Coffman, the conservative Republican mayor of Aurora, Colo., said he was at home on Tuesday night watching the presidential debate and bracing for the worst. And then there it was again, before tens of millions of viewers: former President Donald J. Trump, describing Mr. Coffman’s Aurora, a sprawling suburb just east of Denver, as a city under siege, terrorized by migrants. “They’re taking over buildings,” Mr. Trump said. “They’re going in violently.” Mr. Coffman was contrite on Thursday as he told that story. After all, he had helped create the tall tale now sullying his city’s reputation. Before Springfield,...