Businesses and voters may be gearing up for deregulation by Donald Trump, but a large portion of the country will be displeased with the sacrifices that could come with the rollback, Jeff Sonnenfeld told CNBC on Tuesday.

"There's a proliferation of agencies and we don't see a proper adjustment of regulations, but we're going to be getting rid of some that are quite popular in environmental and health care areas," the Yale School of Management senior associate dean of leadership studies told "Squawk Box." "That'll be a big concern."