Health insurers are privately warning brokers that premiums for many individuals and small businesses could increase sharply next year because of the health-care overhaul law, with the nation's biggest firm projecting that rates could more than double for some consumers buying their own plans.

The projections, made in sessions with brokers and agents, provide some of the most concrete evidence yet of how much insurance companies might increase prices when major provisions of the law kick in next year—a subject of rigorous debate....