Anger over illegal migration helped return Mr. Trump to the presidency, and he has enacted even more aggressive policies than those Mr. Biden first campaigned against. Mr. Trump has drawn outrage from Democrats by sending masked agents to target immigrants, often aided by National Guard soldiers. But a New York Times examination of Mr. Biden's record found that he and his closest advisers repeatedly rebuffed recommendations that could have addressed the border crisis faster, and eased what became a potent issue for Mr. Trump as he sought to return to the White House and justify the aggressive tactics roiling American cities today.