On Jan. 1, the key provisions of the Affordable Care Act took effect. Americans gained access to new health plans subsidized by federal dollars. Insurers no longer can turn away people with existing conditions. Millions are now eligible for new Medicaid benefits.

But the federal law also upended existing health-insurance arrangements for millions of people. Companies worry about the expense of providing new policies, some hospitals aren't seeing the influx of new patients they expected to balance new costs and entrepreneurs...