But one appealing point of leverage for a dealmaker like Trump would be Carrier's parent, United Technologies, a $56 billion company that generates about 10 percent of its revenue from federal government contracts — and particularly from Pentagon defense contracts.
But President Trump will not have as much leverage over those contracts as CEO Trump would have had in the private sector.
Federal contracting regulations are notoriously restrictive. And experts tell CNBC that any effort to quash UTC contracts could run afoul of the rules and expose the federal government to a costly lawsuit from the company.
"You cannot award or fail to award a contract to United Technologies on the basis of any factor that's not mentioned specifically in writing in the original solicitation or the contract itself," said Steven Kelman, a professor at Harvard's Kennedy School of Government and a former administrator of the Office of Federal Procurement Policy in the Office of Management and Budget under Bill Clinton. "Those are the only considerations you are allowed to use."
Kelman said Trump could have considerable leeway in rhetorical bluster, but any effort to punish the company could prove problematic. "I do not think it is legal to use the contracts in this way," he said. "He can say anything he wants, but it would be illegal to do it. And UTC must know that."
All of the rules are spelled out in detail in Part 15 of the Federal Acquisition Regulation, the bible of government contracting doctrine.