With Mr. Trump emphatically rejecting that idea, the best chance for Republicans to secure the White House (and improve their prospects down ballot) may be a different course: Mr. Trump could publicly declare that although he will remain the Republican nominee he will resign immediately after taking his oath of office on Inauguration Day, leaving his more-popular running mate, Mike Pence, to succeed him as president.

In this way, Republicans can effectively replace Mr. Trump at the top of the ticket, without having to endure the logistical and legal turmoil of formally nominating a new standard-bearer less than a month before Election Day.

If Mr. Trump were to drop out before the election, the party would have to fill the vacancy through a vote governed by Republican National Committee rules—a process that would be time-consuming and tumultuous, and that would distract Republicans during the election’s critical home stretch.