And another 15 percent of voters incorrectly believe Obamacare has either been fully repealed, or repealed and replaced with a new health-care law, according to the Morning Consult/Politico survey.
The findings come less a week before open enrollment begins Nov. 1 in Obamacare individual health insurance plans.
Customers on Wednesday could begin window-shopping for those plans, checking out the prices of coverage in their region.
Obamacare advocates have expressed concern that confusion over the law's status, and other factors, will decrease the number of people signing up for health plans that take effect Jan. 1
Part of that confusion stems from efforts since the beginning of 2017 by Republicans in Congress and President Donald Trump to repeal key parts of the Affordable Care Act and replace it with a new law.
"We've been campaigning on it for seven years," Rep. Mark Meadows, R-N.C., told the Morning Consult for a report on the poll's results.
"So I think some people believe that we've executed better than we have," said Meadows, who is chairman of the House Freedom Caucus, a group of conservative House members.
The poll, which questioned 1,988 registered voters from last Thursday through Monday, has a margin of error of 2 percentage points.
The Affordable Care Act continues to require most Americans to have some form of health insurance or pay a tax penalty.
The IRS last week said, for the first time, that it will not accept electronically filed income tax returns that do not disclose if the filer had complied with the ACA's mandate to have health coverage. The agency also said it will suspend processing paper-filed returns that lack that disclosure.
The Morning Consult/Politico poll also found that a broad majority of American voters say that former President Barack Obama — not Trump — is responsible for the current state of Obamacare, and of the U.S health-care system generally.
Only 20 percent of voters said Trump is responsible for the current state of the Affordable Care Act, the health-care law championed by Obama.
And just 28 percent say Trump is responsible for the state of the American health-care system generally.
In contrast, 67 percent of voters said Obama is responsible for the state of Obamacare.
And 50 percent of them said Obama is responsible for the state of U.S. health care.
Trump last week said that Obamacare price hikes for plans that take effect next year are "the fault of the Democrats" like Obama.
The poll also asked voters their opinions of Trump's decision to cut off billions of dollars of government reimbursement payments to Obamacare insurers.
Those payments compensate insurers for discounts granted to low-income customers for their out-of-pocket health costs.
Obamacare premiums are projected to sharply rise due to cut off of the reimbursements, because insurers still must, by law, offer the discounts to customers even though they are no longer getting the money from the government.
A total of 46 percent of voters in the Morning Consult/Politico survey said they disapproved of Trump's move to end the subsidies.
Another 39 percent approved of the decision.
Only 25 percent of respondents said the cutoff of payments would have a positive effect on themselves or their family.
And 39 percent said it would have a negative impact.