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 say they may hire more part-time workers to avoid offering more coverage.

The law’s true impact will play out over years. It will depend in part on whether backers overcome serious early setbacks, including crippling glitches in the new online insurance marketplaces and many states’ rejection of the Medicaid expansion. But another obstacle the law faces is pushback from some consumers and industry over the higher costs, complex rules and mandatory requirements it imposes. ( Watch doctors, business owners and patients share their stories about the health law, and tell us your own. )

So far, 3.3 million have signed up for plans through the new government marketplaces, federal officials said Feb. 12. About 6.3 million were determined eligible for Medicaid through the exchanges over the final three months of 2013, including people who might have been able to enroll without the law.

The law’s potential for change can be seen in the lives of people like Jaime Hood, a 37-year-old in Belton, Mo. She suffers from hemophilia and had been rejected for coverage until this year. Now, she will have access to drugs and other treatments she sometimes skipped.

But the other side of the law is felt by customers such as John Lavey, 60, of Southern California’s Orange County. His insurer sent him a letter in October saying his family’s plan didn’t comply with the law, and the closest thing he could get would cost nearly twice as much, or about $1,117 a month. “It doesn’t seem fair to our situation,” he said. To him, the law feels like “the redistribution of wealth theory.”

Under the health law, the hospital industry said it would accept big cutbacks in government payments in return for the revenue that would come from tens of millions of patients who would gain insurance.

That isn’t happening at Truman Medical Centers, a safety-net hospital system in Kansas City, Mo. Chief Executive John W. Bluford III is slashing expenses—he isn’t seeing the new revenue, mainly because Missouri opted out of the health-law’s Medicaid expansion.

Historians call the Affordable Care Act the most ambitious new social program in a generation. But the debate over the law reflects the tension behind a century of attempts to mandate universal health care. Many Americans are uncomfortable with programs they believe substitute government largess for personal responsibility.

A Kaiser Family Foundation poll in January found that 50% of Americans have an unfavorable view of the health law, while 34% see it favorably.

The law’s fate will depend heavily on people like Tom Daly, a 29-year-old bike-shop owner in Portland, Ore., who is uninsured. Though he sees value in getting coverage, he is likely to pass on it, in part due to the cost. If young, healthy people like him don’t buy policies, with their premiums helping to pay the claims of sicker consumers, the new government marketplaces won’t work.

Erin Patinkin and Agatha Kulaga, owners of a bakery in Brooklyn, N.Y., face decisions about employee coverage, which likely will cost more when they renew it this fall. They say they may employ more part-timers as they expand, since they don’t offer them insurance. Employers’ responses will determine whether the law helps spark a decline in workplace health benefits, as some have forecast.