Bit by bit, the media narrative around the travails of Obamacare and its main enrollment vehicle, HealthCare.gov, is starting to look up. Or to put it more precisely, it is no longer so crushingly negative.

After weeks of stories about website crashes and canceled health plans – and an extraordinary mea culpa from President Obama – a competing story line is starting to emerge. Slowly but surely, people are navigating the exchanges and getting insurance – for some, cheaper and better than what they had. Last week, The New York Times and Los Angeles Times touted a “surge” in enrollment figures, especially in states that have their own exchanges.

This week, a Washington Post story described almost an Obamacare nirvana – people in rural Kentucky lining up and getting coverage, some for the first time in their lives.

Part of this wave of positive stories may be a media effect: Reporters (and the public) get tired of all the wall-to-wall negativity, and to keep interest up, seek out happy stories for a change of pace.

The Obama administration has also ramped up its public relations efforts on the Affordable Care Act (ACA), going around the national media and directly into local markets. On Tuesday, the administration announced that seniors saved $8.9 billion on prescription drugs thanks to the ACA. And Democratic senators have headed off for Thanksgiving with marching orders: Find and publicize the ACA success stories. At the very least, say Democrats, they need to counter the Republican message machine and story-gathering.

“It’s true, the Democrats are more on the offensive than they were,” says Terry Madonna, a professor of public affairs at Franklin & Marshall College in Lancaster, Pa. “But they still have serious problems. No one knows where this is going. And for Democrats, the last thing they want is for this to dominate the elections next year.”

This Saturday, Nov. 30, will be one moment of truth. That is the day the Obama administration promised HealthCare.gov would work smoothly for the vast majority of users, after the disastrous Oct. 1 launch. The definition of “vast majority” was later downgraded to 80 percent – with the remaining 20 percent enrolling by other means or still encountering slow loads and error messages.

On Tuesday, in a conference call with state and local elected officials, Health and Human Services (HHS) Secretary Kathleen Sebelius promised a “significantly different user experience” on HealthCare.gov by the end of the month. And with reporters on the line, she urged the officials “to not hesitate to recommend that people go to HealthCare.gov and get signed up.”

Secretary Sebelius has put her credibility on the line at a time when she can ill afford to see it go any lower. The problem for the Obama administration is that by announcing a hard deadline – Nov. 30 – for vast improvements on a once-profoundly dysfunctional website, it has raised expectations (again) for how well the site will work. As with the initial rollout, Obamacare opponents will be on the lookout for failures, and the media will surely cover them.

Another moment of truth will come when the administration reveals demographic data of people who have enrolled in coverage via the exchanges, possibly with the next official enrollment numbers in mid-December. The ACA will work only if less-healthy enrollees are balanced by enrollees without expensive health issues. On Tuesday’s conference call, Sebelius said she didn’t have demographic information on enrollees, but promised it “very soon.” Then she urged the county executive from Milwaukee to reach out to “young and healthy individuals.”

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The daily report Tuesday from Kaiser Health News (KHN) was noteworthy for its positive stories:

“Health law may offer part-time workers better options,” said one headline. The story talked about “mini-med” plans – low-cost, low-benefit plans that are no longer allowable under the ACA – and cited the case of a woman with a serious health problem who is likely to get better, subsidized coverage on the exchange.

Another piece reported on Californians happy to have their insurance policies canceled. Some people, the story reported, had felt trapped with subpar plans but had kept them because of preexisting medical conditions. Now, under the ACA, people with health problems cannot be denied coverage.

A story out of Philadelphia, highlighted websites that have been set up that allow people to calculate their health-care subsidy without going on HealthCare.gov – and if they’re not eligible, allow them to buy coverage directly from the site.

If they are eligible, however, they have to buy their coverage on the federal exchange. So ultimately, for those living in the 36 states that are served by HealthCare.gov, all roads lead back to that site. Among the challenges ahead for the federal site:

By Saturday, the Obama administration says HealthCare.gov should be able to handle 50,000 users simultaneously. Whether that will be enough capacity is an open question. But it’s safe to say that if too many people wait till the last minute to sign up, there could be another wave of embarrassing website failures.

People who want their insurance to begin on Jan. 1 now have until Dec. 23 to enroll. But again, if everyone waits until Dec. 23, that leaves the insurers just eight days – right during the holidays – to process all that paperwork.

And about that paperwork… The “834” forms that are supposed to go to the insurance companies after consumers enroll on HealthCare.gov still need work, the HHS agency in charge of the site said Monday.

Then there’s the issue of Healthcare.gov’s “back-office system,” which a week ago was still unbuilt. On Nov. 19, Henry Chao, a top official at HHS’s Centers for Medicare and Medicaid Services (CMS), said that between 30 and 40 percent of the IT system for the marketplace remained to be constructed. That sounded alarming, but a CMS spokeswoman said that that portion of the website is involved in paying federal subsidies to insurance companies and will not affect individuals.

Getting HealthCare.gov fully functioning in time still sounds like a high-wire act. If there are more major stumbles, the bad headlines will come roaring back.