Premiums have risen for many years and 43 percent of respondents report higher premiums in the poll for any reason, including the health care law. Again, the percentages are far higher for Republicans and tea party supporters than they are for Democrats or the population as a whole.

The third quarter CNBC All-America Economic Survey finds nearly one in five Americans believe their health insurance costs have gone up because of Obamacare . The answers are highly partisan, but not entirely so. For example, about a third of Republicans and tea party supporters believe they have experienced negative economic effects from the law—about 10 points above the average—but 20 percent of Independents and 11 percent of Democrats are also among the group.

While these are very early days for the nation's new health care law, some Americans are already blaming it for higher premiums and few report much in the way of benefits so far.

Insurance experts say it is possible that insurance rates have gone up already because of the inclusion of new benefits mandate by the law, such as prohibiting limits on lifetime claims and free preventative services. However, Henry Aaron of the Brookings Institution responded that it's "inconceivable" that 18 percent of premiums nationwide have already gone up because of health care. He said it likely reflects some increases but people also responding to headlines.

Some insurers might have raised premiums in anticipation of services mandated by Obamacare, but that those increases should have been small and they account for added services, not simply higher prices. "Premiums go up every year, and it has nothing to do with the Affordable Care Act," he said.

(Read more: Americans downbeat on economy ahead of DC battle)

Another area of controversy: whether employers have reduced workers' hours so they no longer qualify as full-time. Employers with 50 or more full-time workers must provide health care under the new law or pay a fine. In the survey, 3 percent of respondents say they have had their hours reduced because of Obamacare. The margin of error for the poll is plus or minus 3.4 percent, so the actual percentage could be zero or a more significant 6 percent of the population.

Similary, 3 percent of the public reports already having lost their private health care coverage because of the Affordable Care Act. Only 1 percent says they now have health insurance for the first time due to the new law.

The reality of the impact of the health care law on premiums is a matter of debate. In some states, insurance premiums will rise while in others they will fall. Young people will pay more, but also get more government subsidies because they tend to be poorer, while older people and those with pre-existing conditions will pay less. Rich people will definitely pay more. Meanwhile, the new exchanges aren't open yet, so the potential benefits of the program—providing health insurance to the uninsured—would not have shown up yet.

What seems most likely, several insurance experts said, is that there have been effects of the law but that they are magnified by partisanship.

—By CNBC's Steve Liesman. Follow him on Twitter: @steveliesman

