Stranded in Indianapolis on Wednesday after an aircraft malfunction, Donald J. Trump did what any gifted showman with a national campaign to run would do: He brought the presidential circus to him.

Mr. Trump, who is approaching a self-imposed deadline for selecting a running mate, met throughout the day with three finalists for the position — including two, Newt Gingrich and Senator Jeff Sessions of Alabama, flown in solely for that purpose.

A third candidate, Gov. Mike Pence of Indiana, huddled at his home on Wednesday morning with Mr. Trump and his children, Donald Jr., Eric and Ivanka, and son-in-law, Jared Kushner.

In a scene more reminiscent of entertainment television than a standard presidential campaign, a crush of reporters monitored Mr. Trump’s departure from Mr. Pence’s home, and the comings and goings of vice-presidential prospects from Mr. Trump’s hotel throughout the day.