Obama administration officials say the website HealthCare.gov, which users throughout the country struggled to navigate for much of the last two months to sign up for health insurance under the Affordable Care Act, is gradually improving and will meet President Obama’s goal of having a site that works for the majority of users by December 1.

Administration officials say the media narrative of a broken website is outdated, and the woeful initial rollout of the health care law is over and a new phase has started in which most Americans who log on to get health care are able to do so.

In briefings with reporters and public comments over the last week, Obama administration officials have noted several improvements that have been implemented to make HealthCare.gov easier to navigate. For example, as the site is expected to be able to handle 50,000 users at the same time, once that number is exceeded, users can indicate they want to receive an e-mail from HealthCare.gov alerting them when the site is less crowded and then go to it later.

Such changes should prevent people from waiting for hours, as they did in October, as the website was either malfunctioning or running very slowly because it could not handle the number of users who were trying to access it.

“We are definitely on track, ” said Secretary of Health and Human Services Kathleen Sebelius in a conference call this week, adding, the website experience for users “improves every single day.”

Julie Bataille, a top official at the Centers for Medicare and Medicaid Services, the organization that formally runs HealthCare.gov, wrote in a blog post this week, “the vast majority of users will not experience the slow response times, error messages and system outages that characterized their experience in October.”

“The system will not work perfectly on December 1, but it will operate much better than it did on October 1,” she wrote.

At the same time, Obama’s team is lowering expectations. The president is no longer promising HealthCare.gov will work like Kayak.com or such consumer websites, where people can easily compare options and make purchases and rarely have to come back later because the site is at full capacity.  The administration has said that for a large segment of users, particularly those with complicated family situations that make it hard to determine exactly what subsidies they qualify for, the website simply won’t work for them and they should fill out a paper application or call the “Obamacare” phone line.

On Wednesday, the administration announced small businesses won’t be able to enroll online and also must seek alternatives.

In fact, wary of hundreds of thousands of people going onto the Internet and trying to get insurance on Sunday, December 1 (which happens to be both a weekend day and the date when the administration said the website would be working better), Obama aides are urging groups that support the ACA, like Planned Parenthood, not to send huge numbers of people to the website and potentially cause it to be as bogged down as it was in October.

And other challenges remain. Even if they don’t all go to the website on Dec. 1, millions of Americans from the 36 states that rely on HealthCare.gov will likely try to enroll in the days leading up to December 23, the last time a person can sign up for insurance that starts in January. The site has to handle that crush of last-minute users, and the administration will have another political problem if HealthCare.gov is down for hours on end on Dec. 22 or Dec 23.

Also, it remains unclear if parts of the website that connect consumers’ data with insurance companies are working properly, creating another potential problem area next year, when people start actually using their new insurance.

Some websites run by states, such in Connecticut and California, are working well, but others, like Oregon, are struggling like HealthCare.gov. And administration officials still are not sure if enough young, healthy people are enrolling in the health care plans to balance out the number of elderly and sick ones, nor if they can convince Republican-controlled states like Texas to expand their Medicaid programs and offer insurance for low-income people, as the law calls for.