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."



The businesslike approach Trump's administration will likely take to rolling back regulations could seriously stir the pot of environmental activists and health care hawks, Sonnenfeld said.

"Basically, the approach to regulation that the Trump administration is talking about is list all the regulations you have by agency, and let's figure out which ones are the least harmful to people's health, and then if they're job killing, see if we can't repeal them. That's going to lead to a lot of anger," he said.

But businesses at risk of coming under fire by Trump, who has already blasted companies like Ford for moving jobs abroad and aerospace giants like Boeing and Lockheed Martin for the cost of government contracts, must remember a key rule when standing up to him, Sonnenfeld said.

"Trump is fundamentally a pragmatist. I think a lot of the business leaders don't understand: You don't come firing back at him with anger, come back prepared with facts," he said.

"We've seen recently that the aerospace industry and Ford have done well by getting their facts together, so they're coming back with grass-roots legitimacy," Sonnenfeld said.