ObamaCare enrollments are finally taking off, passing the 3 million mark earlier this month. The early hiccups with the federal health exchange website have largely been solved, too, and predictions of a dreaded insurance "death spiral" now seem wildly off.

Not a bad turnaround for a law that seemed broken back in October.

Yet for all the positive ObamaCare news that's come out in the past month or so, a new tracking poll from the Kaiser Family Foundation finds that, among the uninsured, ObamaCare has actually grown less popular since December. Only 24 percent of the uninsured have a favorable impression of the law, while nearly twice as many, 47 percent, say the opposite. That's a sizable shift from one month ago, when the popularity split was 36/46.

Certainly, there's a ton of volatility in Kaiser's survey, so the latest numbers could be statistical noise. But the overall trend — the uninsured souring on the law — is quite clear, and supported by other recent surveys.

ObamaCare is supposed to most benefit the uninsured. So why is that crucial group turning against the law?

For one, it's possible that since they're more directly impacted by the law, they're more familiar with its warts. The federal exchange website was notoriously glitchy in the early going, and overall public perception of the law quickly turned south. That trend was most pronounced among the uninsured, with large majorities of those who visited Healthcare.gov reporting a dismal user experience.

With the site (mostly) repaired, that sentiment could change if the uninsured give the site a second crack and discover a smoother experience.

There's likely also a fiscal element underlying the downward trend. A December CBS News/New York Times survey, for instance, found that almost six in 10 uninsured thought the health-care law would hurt them financially.

Indeed, that could be true for many of the uninsured. In essence, the law is requiring them to either purchase something or pay a penalty for not doing so. With the individual mandate's deadline drawing closer, it's possible that the uninsured are beginning to feel that financial pinch.

Furthermore, some 8 million people are caught in a health-care limbo, too poor to obtain federal subsidies, but unable to tap the law's vast Medicaid expansion since their states aren't participating in it. Twenty-four states, most with GOP governors, declined the Medicaid expansion, effectively denying millions of low-income people access to cheap health insurance.

Other studies have found that even those who were supposed to qualify for subsidies aren't getting them as readily as expected.

Finally, plain ignorance may also be at play here.

Back in September, a whopping 76 percent of the uninsured were largely unfamiliar with the law. And last month, nearly 60 percent still said they hadn't bothered to look up even basic information about potential coverage options. Even now, only 23 percent of the uninsured have visited a federal or state exchange site, according to Gallup.

In other words, it's possible that at least some of the opposition isn't stemming from the law's true impact, but merely to its perceived impact. A huge chunk of the uninsured don't know what the law would do for them, but they don't like it anyway.

That shouldn't be too surprising. More people report seeing negative, rather than positive, media coverage of ObamaCare, per Kaiser. So though a majority of the uninsured say the law hasn't really affected them yet, twice as many (30 percent) say they're worse off under it than those (13 percent) who say they're better off.

Now, the good news for ObamaCare is that half the uninsured still plan to get coverage, according to Kaiser's survey. And with the federal exchange performing much better than before, it's certainly possible the negative perceptions will turn around as the uninsured give it another shot, or try it out for the first time.

In the end, perceptions of ObamaCare won't doom the law; low enrollment would. And on that front, it appears there will be more than enough enrollments to keep the program afloat.