Other public polls have shown support for the law well below 40 percent, yet the GOP has not been able to turn the health law's unpopularity into a broader advantage on the issue of healthcare.
Most respondents in the Morning Consult survey agreed with the Republican argument that costs are a bigger problem than the number of people without health insurance.
But most voters are generally satisfied with their healthcare benefits, according to the survey.
While 58 percent of those surveyed said the biggest problem with the healthcare system is that it's too expensive, 60 percent said they are satisfied with the cost of their coverage.
Even larger majorities said they're satisfied with the value they receive from their health plan and their access to doctors and other providers.
The survey, conducted by a bipartisan pair of pollsters, surveyed 1,000 likely voters. More results, including attitudes toward the healthcare law, will be released throughout the week.