The Obama administration, in a surprise move late Thursday, said the millions of Americans facing insurance cancellations next year won't have to pay a fine if they don't obtain health care coverage.

The major policy shift, outlined in a letter from Health and Human Services Secretary Kathleen Sebelius to Democratic lawmakers, is the latest attempt by the White House to atone for President Obama's broken promise that all Americans could keep their insurance plans under Obamacare.

The delay, which comes on the heels of pushing back enforcement of other core provisions of the Affordable Care Act, also gives Republicans ammunition to argue the president's signature domestic achievement was not ready for prime time.

The last-second change came just before a Monday deadline for consumers seeking Obamacare coverage on Jan. 1.

The White House had previously said that insurers could extend canceled policies through 2014, but many of the largest insurance providers declined to comply with the request.

Republicans of late have pointed out that just 365,000 people had signed up for Obamacare in October and November, just a fraction of those whose plans were canceled. The White House has struggled to combat criticisms that more people would lose coverage than gain it at the start of 2014.

"If you have been notified that your individual market policy will not be renewed, you will be eligible for a hardship exemption and will be able to enroll in catastrophic coverage," HHS said in official guidance to consumers Thursday.

Before the policy change, such plans were available to just a small percentage of consumers under Obamacare.

And insurance companies blasted the announcement from the White House, saying it could disrupt the marketplaces and undermine preparations for the most sweeping change to the health care system since Medicare.

“This latest rule change could cause significant instability in the marketplace and lead to further confusion and disruption for consumers,” said Karen Ignagni, president of America’s Health Insurance Plans, an industry trade group.