"Since I'm in charge, obviously we screwed it up," Obama said at his year-end news conference.
Officials said late on Thursday that people whose insurance plans were canceled because of new standards under the law may claim a "hardship exemption" to the requirement that all Americans must have coverage by March 31, or face a penalty.
The sudden change was announced four days before the federal government's deadline to sign up for coverage that starts on January 1 under the Patient Protection and Affordable Care Act, which was passed in 2010 and set up online exchanges, or marketplaces, for enrollment.
Republicans seized on the latest announcement as further proof that the law known as Obamacare is unworkable, but Obama said it was just a bump in the road.
"I've said before, this is a messy process," Obama told reporters before leaving for Hawaii for the holidays.
Obama said he did not think the waiver for "a relatively small number" of people would shake confidence in the law. "This is essentially an additional net in case folks might have slipped through the cracks," he said.
Obama, whose public approval numbers have dropped to historic lows over the health law's debut, focused on a surge in enrollment in December that was a big improvement on the months since the HealthCare.gov website opened on October 1.
He said that more than 1 million people have signed up so far for new coverage under Obamacare through HealthCare.gov, which serves 36 states, and 14 state-run marketplaces.
More than half of the signups came from the federal website during a December rush, he said. "The basic structure of that law is working. Despite all the problems, despite the website problems, despite the messaging problems, despite all that, it's working," Obama told reporters.
Still, there are lingering problems. Consumers were unable to access HealthCare.gov for a few hours on Friday, a critical time before the December 23 deadline. Officials said they needed to repair a website error that occurred overnight.
'BEGINNING OF THE END'
Part of the backlash against the policy came when millions of people received policy cancellation notices, forcing Obama to apologize for a promise he made that people who liked their insurance policies could keep them under the reforms.
U.S. officials estimated that fewer than 500,000 people would be affected by the new delay in the so-called individual mandate. The mandate is a core part of the law that aims to provide coverage to millions of uninsured Americans.
The announcement raises fairness questions, however, because it gives a subset of Americans relief from the requirement to buy insurance. "It is the beginning of the end of the individual mandate," said Republican Senator Lindsey Graham of South Carolina.
Republicans have opposed the healthcare law as an unwarranted expansion of the federal government.
'DISRUPTION FOR CONSUMERS'
Insurance industry trade group, America's Health Insurance Plans, criticized the change that could divert more consumers away from the new plans offered under Obamacare.
"This latest rule change could cause significant instability in the marketplace and lead to further confusion and disruption for consumers," AHIP President and CEO Karen Ignagni said in a statement.
Legal experts said it was unclear whether the change would spawn successful legal challenges. Nicholas Bagley, law professor at University of Michigan, said he doubted individuals who are ineligible for the exemption could sue, claiming it was unfair that others received the break.
"You can't usually complain that someone else received a benefit that you didn't get and that caused you injury. That's not how courts typically rule."
Still, the change adds confusion for consumers so close to the December 23 sign-up date, a deadline that could triple demand and strain enrollment systems.
The deadline has already been complicated by the decision from a handful of states who run their own insurance marketplaces to extend the sign-up deadline past the December 23 date set by the federal government. MNsure, the insurance marketplace in Minnesota, said on Friday that consumers would have until December 31 to select a plan for coverage beginning January 1.
In the law, there are 14 categories of "hardships" that can be used to get an exemption from the mandate to buy insurance, such as a recent eviction or bankruptcy.
But this is the first exemption prompted by the administration's botched rollout of the law after months of insistence that there would be no delays in implementing the individual mandate. The administration has already pushed back by one year the mandate for employers.
The change announced late Thursday was suggested by a group of Democratic senators, some of whom face difficult reelection campaigns in 2014.
Health and Human Services Secretary Kathleen Sebelius said in a letter to the senators that those people who receive the exemption will have the option to buy "catastrophic" insurance plans - cheaper insurance with a minimal coverage level that, under the law, is normally available only to people under the age of 30.
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