The survey comes as Republicans have taken steps to revive their efforts to pass a bill that would repeal and replace key provisions of the Affordable Care Act.
The poll was taken after Republican leaders in the House canceled a planned March 24 vote on their bill, known as the American Health Care Act, after it was met with opposition from more than two dozen conservative and moderate GOP caucus members. The telephone poll of 1,203 people has a margin of error of 3 percentage points.
More than half of respondents, 52 percent, said they were "relieved" the bill failed to pass, and a total of 44 percent said they were "happy" at that outcome.
A total of 40 percent said they were "disappointed," and 20 percent said they were "angry" about the outcome.
Kaiser noted that despite overwhelming support for the idea that the Trump administration should try to make Obamacare work, "there is no general consensus" on what Trump and congressional Republicans "should do next on health care."
Nearly half of the public, 49 percent, says they should stop working on health care and move on to other issues. Another 45 percent "want them to keep on working on a plan to repeal and replace the Affordable Care Act," according to Kaiser.
The ACA has been credited with expanding health insurance coverage to about 20 million Americans through several provisions, including subsidizing the purchase of private individual health plans, expanding Medicaid benefits to more poor adults and allowing people under age 26 to remain on their parents' health plans.
Obamacare also barred insurers from charging higher premiums to people with health conditions, and established a minimum set of "essential health benefits" that insurers must cover with their plans.
Republicans have criticized the law for driving up individual plan premiums, and leading to plans with high out-of-pocket costs for customers.
The recent bill would have expanded subsidies to more people to buy individual plans, but also would have tended to result in a lower average rate of financial assistance to individuals. And it would have led to reduced federal contributions to state Medicaid programs than would be seen if Obamacare remained in its current form.
Kaiser's survey found that 61 percent of people said that Trump and congressional Republicans would be responsible "for any problems with the Affordable Care Act going forward" because they control the federal government.
Just 31 percent said that former President Barack Obama and Democrats in Congress will be responsible since they are the ones who passed that law.
Those findings are bad news for Trump and some Republican leaders, who have insisted that Democrats will suffer politically from problems with Obamacare. Trump, in fact, has repeatedly claimed that it would be smart politically for him to let Obamacare fail because of that theory.
In other findings, the public remains evenly divided in its views of Obamacare, with 46 percent holding a favorable opinion and 46 percent holding an unfavorable opinion, according to Kaiser.
Read the entire poll results here.
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