WASHINGTON—President-elect Donald Trump’s first big test on immigration will be how to handle the “Dreamers”—young people brought to the U.S. illegally as children whom President Barack Obama protected from deportation. Mr. Trump is already under pressure from both sides.

Administratively, rolling back those protections is among the easiest things Mr. Trump can do on immigration, but politically, it is among the hardest. How he handles the program—known as Deferred Action for Childhood Arrivals, or DACA—will be an early test of how faithfully Mr. Trump plans to adhere to his campaign promises, which include ending the protections.

On Capitol Hill, the president-elect already faces opposition from several Republicans over stripping young people of their protected status, as well as strong support, portending an early showdown within his party.

The 2012 Obama program has about 750,000 participants, who have been given work permits as well as safe harbor from deportation. During the campaign, Mr. Trump vowed to “immediately terminate” the program, calling it unconstitutional.

That could mean revoking the permits immediately or allowing them to expire, as rules require them to be renewed every two years. Revoking the permits wouldn’t necessarily mean participants would be deported, but they would no longer enjoy special protections or be able to legally work.