"I think it's legitimate for them to expect me to have to win back some credibility on this health care law in particular and on a whole range of these issues in general," he said.
Obama has been under enormous pressure from congressional Democrats to give ground on the cancellation issue under the health care overhaul, a program likely to be at the center of next year's midterm elections for control of the House and Senate.
It's unclear what the impact of Thursday's changes will be for the millions of people who have already had their plans canceled. While officials said insurance companies will now be able to offer those people the option to renew their old plans, companies are not required to take that step.
Insurance companies will be required to inform consumers who want to keep canceled plans about the protections that are not included under those plans. Customers will also be notified that new options are available offering more coverage and in some cases, tax credits to cover higher premiums.
Under Obama's plan, insurance companies would not be allowed to sell coverage deemed subpar under the law to new customers, marking a difference with legislation that House Republicans intend to put to a vote on Friday.
Only last week, Health and Human Services Secretary Kathleen Sebelius told a Senate panel she doubted that retroactively permitting insurers to sell canceled policies "can work very well since companies are now in the market with an array of new plans. Many have actually added consumer protections in the last three-and-a-half years."
Republicans were unimpressed with the changes.
House Speaker John Boehner, speaking in advance of the president's announcement, insisted it was time to "scrap this law once and for all."
"You can't fix this government-run health care plan called Obamacare ," he said. "It's just not fixable."
Obama, for his part, made clear he would continue to fight ongoing attempts to sink the whole program, saying, "I will not accept proposals that are just another brazen attempt to undermine or repeal the overall law and drag us back into a broken system."
"We're going to solve the problems that are there, we're going to get it right, and the Affordable Care Act is going to work for the American people," he pledged.
While the White House deals with the cancellation issue, the administration is also promising improvements in a federal website so balky that enrollments totaled fewer than 27,000 in October in 36 states combined. The administration had said in advance the enrollment numbers would fall far short of initial expectations. After weeks of highly publicized technical woes, they did.
Adding in enrollment of more than 79,000 in the 14 states with their own websites, the nationwide number of 106,000 October sign-ups was barely one-fifth of what officials had projected — and a small fraction of the millions who have received private coverage cancellations as a result of the federal law.
[Related: California Dramatically Outperforms Healthcare.gov on Obamacare Enrollments]
The administration said an additional 1 million people have been found eligible to buy coverage in the markets, with about one-third qualifying for tax credits to reduce their premiums. Another 396,000 have been found eligible for Medicaid, which covers low-income people.
Administration officials and senior congressional Democrats expressed confidence in the program's future. "We expect enrollment will grow substantially throughout the next five months," said Sebelius, who is in charge of the program.
"Even with the issues we've had, the marketplace is working and people are enrolling," she added.