WASHINGTON — When President Trump began railing against the current state of American immigration measures over the weekend, it was hard to tell where his thoughts ended and Brandon Judd’s began.

Mr. Judd is the president of the National Border Patrol Council, a frequent guest on Fox News and a reliably vocal supporter of the Trump administration’s hard-line immigration agenda. On Sunday, he was interviewed on “Fox & Friends,” one of the president’s favorite programs.

What followed was a public mind meld with the president, one that has frequently occurred since Mr. Trump took office.

“Our legislators actually have to stand up, and the Republicans control the House and the Senate; they do not need the Democrat support to pass any laws they want,” Mr. Judd said during the segment. “They can go the nuclear option, just like what they did on the confirmation. They need to pass laws to end the catch-and-release program that’ll allow us to hold them for a long time.”