“If Secretary Mayorkas does not resign, House Republicans will investigate every order, every action and every failure to determine whether we can begin impeachment inquiries,” McCarthy said in his own visit to El Paso in November.

For his part, Mayorkas didn’t disagree with the idea that the nation’s immigration system is broken.

“We are dealing within a broken immigration system that Congress has failed to repair for decades,” he told host George Stephanopoulos. “And there is unanimity with respect to that reality.”

On Thursday, Biden unveiled a policy that will accept 30,000 migrants a month from Cuba, Haiti, Nicaragua and Venezuela, the hemisphere’s most troubled nations. “Do not just show up at the border. Stay where you are and apply legally from there,” Biden said, addressing potential migrants from those nations. “Starting today, if you don’t apply through the legal process, you will not be eligible for this new parole program.”

Mayorkas said the entire hemisphere is facing a crisis because of migration, noting huge increases in the populations of both Colombia (from Venezuela) and Costa Rica (from Nicaragua).

“The world is dealing with the greatest displacement of people since World War II in the Western Hemisphere,” he said. “Our entire hemisphere is gripped with a migration challenge.”