Updated

While millions of Americans make a last-minute rush to stores to find one more Christmas present Tuesday, Americans in 36 states are getting one more opportunity to sign up for ObamaCare after the White House extended Monday's deadline by 24 hours.

The deadline to sign up for insurance in order to have coverage by Jan. 1 was supposed to be Tuesday at midnight. But the administration has programmed its systems so that anyone who got in line Monday but takes until Tuesday night to enroll will still get covered by Jan 1.

However, the Centers for Medicare & Medicaid Services tried to downplay the change. A spokeswoman continued to stress that the deadline is technically Monday, even while confirming it would be pushed back to Tuesday.

"The deadline for signing up for coverage to start January 1 is today," spokeswoman Julie Bataille said. "We recognize that many have chosen to make their final decisions on today's deadline and we are committed to making sure they can do so. Anticipating high demand and the fact that consumers may be enrolling from multiple time zones, we have taken steps to make sure that those who select a plan through tomorrow will get coverage for Jan 1."

CMS confirmed the change after The Washington Post first reported it. The acknowledgement came as applicants encountered site problems on Monday, with users being placed in a virtual waiting line when the system was overloaded.

But the agency compared the tweak to Election Day, when people in line when the polls close would still get to vote.

Still, the ObamaCare rollout has been marked by a series of delays, both minor and major. Another, letting those whose plans were canceled sign up for bare-bones coverage, was announced right before the holiday break.

A Republican National Committee spokesman called the latest delay an "opaque move" from an administration that vowed to be transparent.

In Ohio, Republican Lt. Gov. Mary Taylor called the deadline extension "a clear sign Healthcare.gov continues to struggle."

"Consumers are already confused and insurers are overwhelmed with the administration's last-minute changes, yet there seems to be no end in sight," said Taylor, who heads Ohio's insurance department, said.

The administration claimed that the site was running well Monday afternoon, saying Healthcare.gov received a record 850,000 visits, five times the number logged by the same time last Monday. Bataille said the system was handling the volume with error rates of less than 1 in 200 and response times of less than one second.

Obama said on Friday that more than 1 million Americans had enrolled for coverage since Oct. 1. The administration's estimates call for 3.3 million to sign up by Dec. 31, and the target is 7 million by the end of March. After that, people who fail to buy coverage can face tax penalties.

Minnesota, one of the states running their own insurance exchanges, extended its Monday deadline to Dec. 31 amid problems with its website and extra-long hold times to reach its help center. Maryland pushed back its cutoff date to Dec. 27. New York extended its deadline to midnight Tuesday.

The Associated Press contributed to this report.