The first survey, from Public Policy Polling, found that 61 percent of Americans believe that everyone in the U.S. at similar income levels should be able to get Obamacare subsidies regardless of where they live.
Support for that idea was strongest among Democrats, at 74 percent. But even a plurality of Republicans favored keeping subsidies for HealthCare.gov customers—49 percent in support, and 41 percent opposing the idea.
A total of 62 percent of people surveyed by Public Policy Polling favored the Republican-led Congress taking action to continue HealthCare.gov subsidies if the Supreme Court rules they are illegal.
The poll also found that a similar percentage of voters would be more likely to vote for an elected official who worked to maintain the subsidies.
Public Policy questioned 530 registered voters for the poll, which has a margin of error of +/- 4.3 percent. The poll was done on behalf of the progressive group Americans United for Change, which supports Obamacare.
Read MoreThe price of medical care in the US
But the other survey, a Washington Post-ABC News poll, had similar findings. In that poll, 55 percent of respondents said the Supreme Court should not end the HealthCare.gov subsidies, while 38 percent said that aid should be ended.
However, The Washington Post poll also found that a majority of Republicans, 55 percent, favored ending the subsidies.
The survey showed that despite the overall support for keeping the HealthCare.gov financial aid intact for eligible customers, a majority of 54 percent oppose the Affordable Care Act, the health-care reform law that authorizes both the insurance marketplaces and the federal subsidies that help most of their customers purchase health coverage.
The Washington Post noted that level of opposition, which is 6 percentage points higher than a year ago, is the "among the worst" level of support for Obamacare in the poll's history. The survey questioned 1,001 adults, and had a margin of error of +/-3.5 percent.