On an oven-hot day this month, Attorney General Jeff Sessions strode into a hotel ballroom to preach Trump-era immigration gospel to cowboy-hatted sheriffs from 31 counties near the United States’ border with Mexico.

“It is only reasonable that a good and decent people, as the Americans are, to want to end the illegality, to create a rational immigration flow and protect the nation from criminals,” he said, rising a bit on his toes behind the lectern as about 100 attendees stood to applaud at a joint meeting of the Texas Border Sheriff’s Coalition and the Southwestern Border Sheriffs’ Coalition. He added, “A great nation cannot allow this lawless disgrace to continue.”

Javier Guerra, the police chief in Sunland Park, N.M., wanted more specifics from Mr. Sessions.

“I think everybody felt he had to watch what he was saying so he didn’t make the president look bad,” Mr. Guerra said in a later phone interview, reflecting on Mr. Sessions’s speech. “When you’re walking around with an ax in back of your neck, you have to be careful.”