WASHINGTON—The tax overhaul that President Donald Trump signed into law last month capped a year in which his initiatives on taxes, regulation—and many of his public pronouncements on the economy—have been broadly welcomed by business.

It hasn’t all been smooth sailing for the president most closely aligned with business interests in decades: he was roundly criticized for his remarks about a deadly white supremacists’ rally in Charlottesville, Va., last August. After that, several CEOs resigned in protest from his business...