The poll also found strong distrust of Trump's health-care goals — and that half of Americans will blame the Trump administration's actions to weaken Obamacare if fewer people sign up for individual health insurance plans this enrollment season.
Just 37 percent said any fall-off in enrollment would be the fault of the Obama administration and Democrats in Congress, who created the Affordable Care Act, as Obamacare is formally known.
The findings also come three weeks into the first full Obamacare enrollment season under the Trump administration.
Trump and most congressional Republicans favor repeal of much of the ACA. Despite months of efforts this year, they have been unable to win approval of a replacement.
Since Trump took office in January, his administration has made a series of moves to undercut Obamacare. Those actions have been blamed for driving up prices for Obamacare plans in 2018 and for spurring some insurers to drop out of ACA marketplaces. They also have raised concerns among advocates for the law that enrollment in Obamacare plans will fall in 2018.
Trump and his health-care officials have repeatedly said that any problems with the program are the fault of Democrats who passed the ACA into law.
While Trump's health-care policy goals are popular with many Republican voters, the public as a whole does not tend to think highly of them.
Sixty percent of respondents "do not trust President Trump to do what's best when it comes to health care in this country," Kaiser said in a summary of the poll's results.
And majorities of people of all political affiliations say that because Trump and Republicans are in control of the federal government, "they are responsible for the health care law moving forward."
Just 27 percent said that Obama and Democrats are responsible for any future problems with the law.
Among all respondents, 50 percent have a favorable view of Obamacare and 46 percent hold an unfavorable view.
Most Republicans, 81 percent, hold an unfavorable view, while 80 percent of Democrats like the law.
Independents are split, with 50 percent seeing the law unfavorably and 43 percent holding a favorable view.
Kaiser's poll, which had a margin of error of 3 percentage points, questioned 1,201 adults via telephone from Nov. 8 to 13.