California said 28,699 people were signed up in the state’s health-insurance exchange in the first week, while New York had more than 40,000 sign up.

The numbers for California, the largest U.S. state by population, were for the Oct. 1 to Oct. 5 period and exceeded expectations, Peter V. Lee, executive director of Covered California, said at a news conference today in Sacramento. New York, the third most-populous state, said in a statement that its pace of sign-ups shows the exchange is “working smoothly.”

The Oct. 1 rollout of the Affordable Care Act exchanges has faced technical issues, with consumers unable to access parts of the U.S. government’s website that serves people in 36 states. California, one of 14 states running its own website, has fared better. Success is critical in California, where the Obama administration has sent almost $1 billion in exchange grants.

“Looking back at this one week, the response has been nothing short of phenomenal,” Lee said. “We anticipated we’d have very low enrollment in the first week.”

Open enrollment ends March 31, and Lee estimated that 500,000 to 700,000 Californians would enroll with subsidies by then. About 5.3 million Californians will have access to coverage through the exchange or on their own, with about half eligible for financial assistance by next year, according to the state’s website. An additional 1.4 million will be newly eligible for the state’s Medicaid program.

Almost 2.7 million New Yorkers don’t have health insurance and more than 1 million will get coverage through the exchange, the state said on its website. The 40,000 figure reported is for people who completed the full application process and were found eligible for an insurance plan.

The insurance exchanges are a core part of the 2010 law that seeks to provide health coverage for most of the 48 million uninsured Americans. People using the exchanges can select from health plans sold by private insurers and, depending on income, may be eligible to have their premium costs subsidized with federal tax credits. Some people also may be eligible for coverage under an expansion of Medicaid, the joint state-federal plan for the poor.

The health law championed by President Barack Obama has been the focal point of the partisan budget dispute in Congress that led to the current government shutdown.