President Trump entered the White House in January promising both the “largest deportation program in American history” and a “golden age” for American businesses.

But in recent weeks, the tension between those two promises has spilled out into the open, leading Mr. Trump to reverse or contradict some of his most significant anti-immigration policies when they threatened to disrupt the economy.

Mr. Trump has celebrated his success in driving down illegal border crossings and in cracking down on immigration more broadly. But he walks a careful line when his hard-line policies collide with his economic agenda — particularly when it comes to foreign workers, student visas and industries that rely on immigrant labor.

The changing positions have not only infuriated his far-right allies, but have also confused those aiming to carry out his deportation policies.

“His heart isn’t in the nativist purge the way that the rest of his administration’s heart is into it,” said David J. Bier, the director of immigration studies at the Cato Institute. “He’s always been someone who likes to dabble in that type of rhetoric. But at the same time, he’s always had a soft spot for the economic needs from a business perspective.”