They still trust Obama more than Romney to handle it, they still want universal insurance coverage, and many of them feel the law didn't go far enough.

Sometime this month, the Supreme Court will hand down its ruling on the Affordable Care Act, the massive health-care reform law better known as Obamacare. That's inspired a flurry of polls to gauge public opinion about the law. Broadly, the polls reveal that Americans remain deeply uncomfortable with large parts of the law, especially the individual mandate. But it's not that simple. Here's a rundown:

1. National Journal, June 4

Topline: 74 percent say the Supreme Court should strike down the individual mandate.

This Is Weird: Surprisingly, a majority of respondents (51 percent) say the Justices should strike down a key clause of the law, which bars insurers from rejecting customers on the basis of pre-existing conditions and was broadly popular with Republican as well as Democratic lawmakers. Furthermore, 46 percent say that if the law is struck down, they want Congress to try again to produce a law that guarantees insurance for almost all Americans. That suggests one of two outcomes. One is that there's a desire for a far more liberal law -- the individual mandate, which is three in four oppose, was a conservative alternative to publicly provided insurance. Any expansion would likely require government to take a larger role. The second possibility is that most Americans just don't understand the law.

2. CNN/ORC, June 8

Topline: 51 percent of respondents oppose the Affordable Care Act.

This is Weird: There's more to that 51 percent figure than meets the eye. It turns out that only one in three feel the law was "too liberal" (to use CNN's somewhat slippery language). One in six said they objected to the law because it didn't go far enough. And get this: A solid 5 percent don't like the law but can't explain why (see above, "most Americans just don't understand the law"). It's worth noting that support in CNN's poll has been steadily growing for the last year and now sits at 43 percent.

3. Fox News, June 7

Topline: 52 percent say the Obama administration has "mostly failed" at improving health care.

This Is Weird: Despite that failure, more voters (43 percent) trust Obama to handle health care than do Romney (40 percent).

4. New York Times/CBS News, June 7

Topline: Just 24 percent say they want the law to stand. Four in 10 want the whole shebang overturned, while another quarter just want the individual mandate eliminated (again, it's unclear how the expansion of coverage would be paid for without the mandate).

This Is Weird: Once again, the poll punctures conventional wisdom about why Americans oppose the law. The spread between the percentage who think the law goes too far (37 percent) and those who think it's not sweeping enough (27 percent) is just 10 points.