Health insurance premiums may as much as double for some small businesses and individual buyers in the U.S. when the Affordable Care Act’s major provisions start in 2014, Aetna Inc.’s chief executive officer said.

While subsidies in the law will shield some people, other consumers who make too much for assistance are in for “premium rate shock,” Mark Bertolini, who runs the third-biggest U.S. health-insurance company, told analysts Wednesday at a conference in New York. The prospect has spurred discussion of having Congress delay or phase in parts of the law, he said.