Senator Cory Booker, tieless and in a blazer on the southwestern border in early July, approached a Customs and Border Protection officer, blue passport in hand. They greeted each other and the officer asked: “Is there somebody with you?” Yes, Mr. Booker said, he had a group with him.

Specifically, Mr. Booker said, he was traveling with a group that included five women, all survivors of domestic violence in their home countries, Cuba and Honduras, who were seeking asylum in the United States. They had been sent back to wait in Mexico once before.

But now they had a high-profile senator and 2020 presidential candidate with them, and he had a slew of cameras and reporters waiting across the border for him.

Those cameras were on hand to capture the women walking across the bridge from Mexico, and were around later to hear the senator announce that the women were allowed to continue into El Paso and take refuge in a shelter while their applications would be processed. He stayed on a street corner to answer questions from reporters for about 10 minutes.