Some low- and middle-income families will be eligible for federal subsidies to help offset those costs.
Virtually every American will be required to buy some form of health insurance by Jan. 1. Those who receive coverage from their employers or through an existing government program, such as Medicaid and Medicare, won't use the exchanges.
Winifred Okwuchi, a 19-year-old student at Prince George's Community College, said she found Obama's address "powerful" but also instructive.
She said she is insured under her parents' health plan — the law allows children to stay on their parents' plans until they turn 26 — but she would consider signing up for coverage through the exchange if needed later.
"I feel like it's going to help us in the long run," she said. "It's a starting point for us after we move off our parents'" insurance.
The exchanges are being created by the state, but the policies are sold by private insurers. The exchange will allow consumers to compare private plans in the same way that websites allow travelers to compare airfares before they buy tickets.
Supporters of the law are particularly eager for young, healthy people to sign up for coverage, because their participation is expected to reduce premiums for all participants.
Rep. Donna F. Edwards, a Democrat whose district includes the college where Obama spoke, implored students to sign up. She said she didn't have coverage when she was young, and she almost lost her home when she got sick and had to go to the emergency room.
"You sign up because it's the right thing to do and it's the right thing to do for your families," Edwards said.