Almost one-third of respondents in the online survey said they prefer Democrats' plan, policy or approach to health care, compared with just 18 percent for Republicans.
The poll, conducted after the White House announced that more people than expected had signed up for the Affordable Care Act, marks an increase in support for Democrats and a slide for Republicans since a similar Reuters/Ipsos poll in February.
One-fifth of respondents said they didn't know which party had a better plan, and another fifth in the survey released Tuesday said neither party did.
The Obama administration has said 7.1 million people signed up for Obamacare by the end of March. Former Health and Human Services Secretary Kathleen Sebelius said before resigning last week that she expected the number to rise to 7.5 million by the end of the year.
"In the last couple of weeks, as the [health care] exchanges hit their goals, news coverage has been more positive and the support of the Democratic Party on this issue has rebounded," said Ipsos pollster Chris Jackson.
"It's not that independents are moving their way, it's that Democrats who had previously been a little bit ambivalent in their support are coming back to the party."
Obamacare has been under heavy fire from Republicans, particularly after the trouble-plagued healthcare.gov website went live in October. But the poll suggests many Americans believe that Republicans haven't offered a substantial health care alternative.
"Democrats have not managed to have a huge lead over Republicans so much as Republicans have managed to damage their own position and stay behind Democrats," Jackson said. "That's because people don't view the Republican Party as standing for any particular healthcare system."
In a Reuters/Ipsos poll from February, about one-quarter of respondents said Democrats had a better plan. That number increased to 31 percent in March and 32 percent in April.
Republicans' health care plans were supported by 24 percent of respondents in the March survey — six percentage points higher than their April support.