Nearly 2-million people visited healthcare.gov yesterday.
The centers for Medicare and Medicaid services say they also received more than 250,000 calls.
The deadline to sign up for insurance to be covered on January 1 was midnight, but it was extended through today, in case of heavy demand on the government website.
Healthcare.gov serves 36 states.
The president, meanwhile, signed up for health insurance through a health exchange created by the law.
The White House says President Obama signed up through the Washington DC marketplace over the weekend.
It's unclear if he encountered any of the glitches millions of Americans have experienced.