WASHINGTON — The choice by President Trump of a pro-immigration economist to lead his Council of Economic Advisers is stirring a backlash among his most ardent supporters, who worry it is an abandonment of the tough stance he took on the issue during the campaign and the latest in a string of broken promises.

Mr. Trump had already disappointed some of his base supporters by intervening in Syria with a military strike last week and by delaying a tough stance on trade with China and Mexico. He expressed the idea via Twitter on Tuesday morning that he would be willing to offer the Chinese government a more favorable trade deal if it helped the United States with North Korea. Now there is growing unease that immigration is the next area where he will go soft.

To these supporters, the appointment of Kevin A. Hassett, announced late last Friday afternoon, as Mr. Trump’s top White House economist is another sign that the president is succumbing to the swamp he promised to drain.

Like most economists, Mr. Hassett believes that immigration spurs economic growth. At times he has pilloried Republicans for becoming the “Party of White,” arguing in 2010 that Republicans like then-Gov. Jan Brewer of Arizona “have too often appeared hostile to immigrants.” In 2013, Mr. Hassett said the United States should double its intake of immigrants.