The poll released Friday comes a day after Trump dropped a bombshell on those marketplaces by cutting off billions of dollars of federal reimbursement payments to Obamacare insurers.
The Kaiser Family Foundation survey was conducted in the week before Trump's decision to kill those so-called cost-sharing reduction payments, a decision that is expected to lead to much-higher individual insurance plan premiums in the next several years.
The poll found that 60 percent of the public supported Congress guaranteeing those CSR payments "to help stabilize the insurance market."
"One-third think these payments amount to a bailout of insurance companies and should be stopped," the Kaiser Family Foundation said in a report on the poll.
But a total of 69 percent of respondents favored the idea of having Congress guaranteeing the CSR payments if it were part of a bipartisan legislation that would also give states more flexibility in the types of plans that can be sold on Obamacare marketplaces.
The CSRs compensate insurers for discounts in out-of-pocket health charges they must offer, by law, to low-income Obamacare customers.
The Trump administration said Thursday night the reimbursements to insurers for those discounts are illegal because the payments were not specifically authorized by Congress.
So from now on, unless Congress authorizes the money, insurers will still have to charge low-income customers less for their out-of-pocket costs without getting compensated by the government for those discounts.
The Kaiser poll found that 66 percent of Americans said it was more important that Trump and Congress work on legislation to bolster the marketplaces than to continue their efforts to repeal and replace major parts of the Affordable Care Act.
Despite that strong support, 70 percent of Americans said they were either "not too confident" or "not at all confident" that Trump and Congress will be able to work together to make improvements to those marketplaces.
The poll found that strong majorities of Democrats and independents favored steps that would support Obamacare.
In contrast, Republicans, as a group, tended to oppose such steps, albeit less strongly than Democrats supported them.
However, 68 percent of Republicans favored the idea of Congress guaranteeing the CSRs as part of bipartisan legislation to give states more flexibility in their Obamacare marketplaces. That was just one percentage point less than the share of Democrats who backed that idea.
The poll was conducted from Oct. 5 through Tuesday, and questioned 1,215 adults over the phone. The poll had a margin of error of 3 percentage points.