WASHINGTON — Computer crashes should be giving way to insurance coverage — if the government’s diagnosis of its health care website is correct.

The Health and Human Services Department released a progress report Sunday on its effort get the troubled HealthCare.gov website on the mend. Administration officials said the worst of the online glitches, bugs and delays may be over.

“The bottom line — HealthCare.gov on Dec. 1 is night and day from where it was on Oct. 1,” said Jeff Zients, the White House’s troubleshooter tasked with making the website function properly.

Yet officials acknowledged more work remains on the website, which made its national debut two months ago with hundreds of software flaws, inadequate equipment and inefficient management. Federal workers and private contractors have undertaken an intense reworking of the system, but some users might still encounter trouble.

How many problems are left? That’s the

question consumers and lawmakers alike will be eying before the next crucial deadline: Dec. 23.

That date is likely to be the first big test of the repaired website, as consumers rush to meet the deadline so their coverage can kick in on the first of the year.

“There’s not really any way to verify from the outside that the vast majority of people who want to enroll can now do so, but we’ll find out at least anecdotally over the coming days if the system can handle the traffic and provide a smooth experience for people trying to sign up,” said Larry Levitt, a senior adviser at the Kaiser Family Foundation.

But, he added, HealthCare.gov is clearly working better than when it first went online. Its challenge now is to convince users who were frustrated during their first visit to give it another chance.

HealthCare.gov was envisioned as the principal place for people in 36 states to buy insurance under President Barack Obama’s health care law. But its first few weeks were an embarrassment for the administration and its allies.

Obama made Dec. 1 a self-imposed deadline to fix several significant problems and the administration organized a conference call with reporters Sunday to boast that 400 technical problems had been resolved. Officials, however, declined to say how many items remain on the to-do list.

Even with the repairs in place, the site still won’t be able to do everything the administration wants, and companion sites for small businesses and Spanish speakers have been delayed. Questions remain about the stability of the site and the quality of the data it delivers to insurers.

Obama promised a few weeks ago that HealthCare.gov “will work much better on Nov. 30, Dec. 1, than it worked certainly on Oct. 1.” But, in trying to lower expectations, he said he could not guarantee that “100 percent of the people 100 percent of the time going on this website will have a perfectly seamless, smooth experience.”

Obama rightly predicted errors would remain. The department reported the website was up and running 95 percent of the time last week — meaning a 1-in-20 chance remains of encountering a broken website. The government also estimated that pages crashed at a rate less than once every 100 clicks.

But the administration gave itself a passing grade for meeting its goal of allowing 50,000 people to log onto the website at one time and more than 800,000 people to shop for insurance coverage each day.

If true, it’s a dramatic improvement from the system’s first weeks, when frustrated buyers watched their computer screen freeze, the website crash and error messages multiply.

The figures — which could not be independently verified — suggest millions of Americans could turn to their laptops to shop for and buy insurance policies by Dec. 23.

The nation’s largest health insurer trade group said significant problems remain and could be a barrier for consumers signing up.

“HealthCare.gov and the overall enrollment process continue to improve, but there are significant issues that still need to be addressed,” said Karen Ignagni, president and CEO of America’s Health Insurance Plans.