Five years after the passage of Obamacare, it's starting to look like more Americans may slowly be coming around to the idea of supporting the health care law. A greater number of Americans still oppose the Affordable Care Act than support it, but that margin has narrowed to its lowest point in more than two years, according to a new poll.

Forty-three percent of Americans this month view the law unfavorably, while 41 percent give it a favorable rating, according to the Kaiser Family Foundation's tracking poll. According to Kaiser data, overall opinion on the law has been improving over the past few months, which saw a much smoother Obamacare enrollment season compared to last year, with fewer glitches.

A deeper dive into the polling numbers, though, shows a more complicated picture. The number of uninsured has plummeted, but that success hasn't translated into broad popularity for the law. Partisan views are entrenched. And there's declining optimism among those expected to benefit most from the health-care law's coverage expansion, Kaiser's polling data show.

Racial support for the law

The health-care law has continuously received strongest support from minority groups, while whites have consistently had a more negative opinion on the law. And support among white Americans has slipped over time. The latest March numbers show that 53 percent of whites viewed the law unfavorably, up from 48 percent right after the law was passed in April 2010. Thirty-four percent view the law favorably in the March poll, down from 39 percent after the law was passed.

Among Hispanics, as you can see below, support for Obamacare has been strong since the law's passage, though it has dropped since then. More than two-thirds viewed the law favorably in April 2010, almost four times the rate of Hispanics who had unfavorable views. But now, just under half of Hispanics — who have the highest uninsured rate of any ethnic groups — view it favorably.

"Hispanics definitely in the last five years have trended toward the less favorable view," said Mollyann Brodie, who heads Kaiser's polling operation. "I don't think we have a good sense of why, other than we know that many Hispanics are not actually helped by the law." Opinions on the ACA are also closely aligned with political identity, and she pointed out that Hispanics are less tied to the Democratic party.

Meanwhile, African Americans have been much more consistent in their ACA support, with two-thirds saying they see the law favorably in March — about where the group stood right after the law's passage. Even fewer African Americans view the law unfavorably now, compared to then.

Support among the uninsured

Among those with insurance, views of the law have remained pretty steady over the past few years. But favorability has been steadily creeping up in the past six months, and those with insurance this month view the law more favorably (just slightly, though) for the first time since Obama's re-election in November 2012. Some of this support could be coming from Americans who are newly insured thanks to the law.

Meanwhile, as the ranks of the uninsured have dropped by historic rates since Obamacare's coverage expansion took effect early last year, those who remain uninsured have been souring on the law. The uninsured over the past two years were more likely to have a unfavorable view of the law, a change from the ACA's first few years.

The poll does not specify where respondents live, leaving us to guess how many of the uninsured who view ACA unfavorably aren't happy that their governors or state legislatures have refused to participate in the expansion of Medicaid.

Of course, the pool of uninsured is different now than it was two years ago. "They're the long-term [uninsured]," Brodie said. "They're a more challenging population to insure."

Those who remain uninsured are pessimistic about their chances of getting coverage. Almost half (44 percent) of the uninsured said they don't expect to get health insurance in the next few months. About two-thirds of the uninsured last year didn't bother to look for coverage, largely because they didn't think they could afford it, according to an earlier Kaiser survey. And many who'd likely qualify for financial assistance under the ACA remain unaware that it's available.

Kaiser's polling shows that the uninsured are also overestimating the negative impact of the financial penalty from the ACA's individual mandate than the provision's likely impact. About 60 percent of the uninsured said they expect to pay the penalty for not obtaining health insurance — but the nonpartisan Congressional Budget Office expects just 13 percent of uninsured Americans will pay a penalty because most will qualify for exemptions.

Five years into one of the most scrutinized laws in recent memory, there's still a lot that the people most likely to benefit from Obamacare don't know about the health care overhaul.