WASHINGTON — It was the morning after another breathtaking revelation about President Trump and a $130,000 payment to a pornographic film actress, and dozens of reporters crowded into the White House Rose Garden, seeking answers. When one of them shouted a question about the payment, the president simply walked away.

Standing nearby, on a ceremonial balcony overlooking the West Wing, was another reporter, David Brody, waiting for a private interview with Vice President Mike Pence.

Mr. Brody, the chief political correspondent for the Christian Broadcasting Network, was not there to inquire about porn stars. It was the National Day of Prayer, and Mr. Brody asked the vice president whether he was tired of defending his anti-abortion views amid “potshots” from comedians, and whether prayer was “alive and well in the White House.” He inquired whether Mr. Pence would attend the opening of the American embassy in Jerusalem, which took place on Monday.

Mr. Pence smiled and answered each question. Then he invited Mr. Brody to get coffee.

“The access has been phenomenal,” Mr. Brody said later in an interview. “I’m very appreciative to God for allowing it.”