A big hurdle for the effort: As recently as last month, three-fourths of the uninsured didn't know there was a March 31 deadline, according to polling conducted for the Kaiser Family Foundation. Most said they didn't know much about the law and had an unfavorable opinion of it.
Plus, many worry they won't be able to afford the new plans.
The enrollment campaign is emphasizing that subsidies are available on a sliding scale to help low-income and middle-class households pay for their insurance.
How to enroll? Start at HealthCare.gov or by calling 1-800-318-2596. Residents of states running their own marketplaces will be directed there; people in other states go through the federal exchange.
After March 31, many people won't be able to get subsidized coverage this year, even if they become seriously ill.
The next open enrollment period is set to begin Nov. 15, for coverage in 2015.
There are exceptions. The big one is the Medicaid program for the poor. People who meet the requirements can sign up anytime, with no deadline.
Also, people remain eligible for Medicare whenever they turn 65.
If you are insured now and lose your coverage during the year, by getting laid off from your job, for example, you can use an exchange to find a new policy then. People can sign up outside the open enrollment period in special situations such as having a baby or moving to another state.
You can choose to buy insurance outside the marketplaces and still benefit from consumer protections in the law.
People who do that wouldn't normally be eligible for premium subsidies. But the Obama administration says exceptions will be made for people whose attempts to buy marketplace insurance on time were stymied by continuing problems with some enrollment websites.
Millions won't get covered