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But even on the foreign policy front, developments this year have included setbacks, including the ceaseless international uproar over Edward Snowden’s spying revelations and the rising tensions in the Middle East, from Syria to Egypt.

Mr. Capretta, a former Bush administration official who focuses on health care policy, said there are likely more problems to come with Obamacare because relatively healthy people will be reluctant to enroll for coverage they don’t need. He also said Mr. Obama’s proposed “fix” for people whose policies were canceled — calling on insurers and state officials to restore substandard plans for one year — isn’t a workable solution.

“I thought it was completely lawless,” Mr. Capretta said. “They’re just making it up as they go. They’re just saying essentially, ‘These plans are still illegal under our law, but we’ll let them happen anyway.’ It’s not really a way to run a country. They really should be working with the Congress to do a legislative fix.”

Ms. Brazile said the politics of the situation won’t change “until the policy is fully understood and implemented without malfeasance by those simply opposed.”

“Once the website is properly working and folks who need access feel more comfortable accessing, the president will have to demonstrate how this new federal program will help those who need it as well as those who might not want it,” she said. “Can the insurance companies do the same? Can Republicans explain why they want people without [insurance] to keep showing up at the emergency room when they get sick?”