WASHINGTON — Anticipating more health care disruptions, the Obama administration Thursday announced a batch of measures intended to help consumers avoid lapses in their care and coverage as the president’s overhaul takes effect in January.

Health and Human Services Secretary Kathleen Sebelius also announced a one-month extension of a special insurance program created by the law for people who cannot get coverage because of health problems. Scheduled to expire at the end of the year, the Pre-Existing Condition Insurance Plan will remain in place through January.

Some of the measures are binding, such as requiring insurers to provide coverage on Jan. 1 for any customer who pays by New Year’s Eve. Others are recommendations, like urging insurers to let customers temporarily keep filling prescriptions covered by a previous plan.

The steps are the policy counterpart to the technical repairs that finally got the HealthCare.gov website working reasonably well. They’re intended to help make sure anyone who needs and wants coverage by Jan. 1 can get it, even if they got trapped by website woes. That includes some of the more than 4 million people whose existing health individual health plans have been canceled because the plans didn’t meet the new law’s requirements.

“That is frankly the big question right now,” said Larry Levitt, an insurance market expert with the nonpartisan Kaiser Family Foundation. “Can the system handle signing up everyone who wants coverage by Jan. 1? I’d say the highest priority is avoiding a gap in coverage for people who are already insured.”

Although intended to help, the new measures may just make things more confusing for consumers since some are mandatory and others voluntary. And the 14 states running their own insurance markets can make their own tweaks.

Among the provisions:

n Strongly encouraging insurers to refill prescriptions covered under previous plans through January. Along with that, the administration also encouraged insurance companies to allow patients dealing with an acute illness to keep their current doctor.

n Following through on a previous announcement by formally setting Dec. 23 as the last day to apply so coverage will take effect Jan. 1.

n Advising consumers who got bogged down with the HealthCare.gov website that they still may be able to enroll after Dec. 23 and get coverage on an expedited basis, if the issue was caused by technical problems.