WASHINGTON - As Americans scrambled to beat a deadline to sign up for insurance under President Barack Obama's healthcare law, the White House gave most consumers an extra day, until Tuesday, to obtain coverage that starts January 1.

The last-minute move by the Obama administration to accommodate high demand came as it reported record traffic on HealthCare.gov, the federal enrollment website that struggled with glitches after its launch in October.

It was the latest impromptu change the administration has imposed on the healthcare program to address the fallout from a series of technical and political missteps.

Officials said the website received 1.2 million visits over the weekend and had surpassed 1 million additional visits by late afternoon on Monday. They said a call center took 200,000 calls from those seeking insurance under the Affordable Care Act, known as Obamacare.

The hustle to sign up in time for January 1 coverage could help the Obama administration as it tries to patch up a botched rollout of the president's top domestic policy achievement, a law that requires most Americans to get health insurance or face fines.

Before the Monday rush, well over 1 million people had signed up for private coverage through HealthCare.gov - which serves 36 states - and 14 state-run marketplaces, according to state and federal estimates. The figure, though likely to climb by Christmas, shows how far the government has to go to reach an estimated 7 million people by the end of enrollment in March.

Obama was embarrassed that HealthCare.gov did not work for most people shopping for insurance for its first two months. He also wound up apologizing for promising that everyone who liked their existing insurance could keep it under Obamacare.

The backlash has torpedoed Obama's approval ratings, alarmed congressional Democrats facing re-election in 2014 and given a boost to Republicans opposed to the healthcare law.

The administration instituted a series of "fixes," but the resulting patchwork of exceptions and deadlines has created confusion among consumers and upset insurance companies that fear the mixed messages could threaten the delicate financial formula around which Obamacare is designed.

On Monday, administration officials continued to encourage uninsured and under-insured Americans to enroll in Obamacare by midnight and said those who sign up before Christmas Day would be eligible for coverage starting January 1.

"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 January 1," Julie Bataille, a spokeswoman for the Centers for Medicare and Medicaid Services, said in a statement.

She was echoed by White House spokeswoman Jennifer Palmieri, who warned that waiting until Tuesday to start enrolling in Obamacare would be risky.

"People should not think that they can get on the website (Tuesday) for the first time and try to enroll," Palmieri said in an interview on MSNBC. "That would be a dangerous thing to do."

In a mid-morning Twitter post on Monday, HealthCare.gov touted "a record day so far".

"Thousands visiting and enrolling now. Queuing deployed to help keep site smooth for users," the post said, referring to a system that sends users to an online "waiting room" when web traffic runs high.

"There is definitely a rush!" said Lauren Banks of AIDS Alabama, part of Enroll Alabama, one of dozens of "navigator" groups that is helping people sign up for coverage. "People lost track of time, and suddenly (the deadline is) here."

Navigator group SER National in Illinois said its Obamacare sign-up events are now attracting hundreds of people compared with dozens in October and November.

SER's navigator program director Zeke Romo said the last-minute shoppers include "a lot of people with complicated medical issues, such as people with children who are on medication" and are worried about a break in coverage if they don't sign up in time for January 1 benefits.