"It would be unfair to allow families to lose their coverage, particularly in the middle of the year," Hatch's op-ed said.
But Hatch's plan was short on details. And it's not clear that any proposal of his would survive a vote in Congress controlled by his party.
Read MoreBig Obamacare price hikes could be coming soon
Even as Hatch and other leaders propose funding the subsidies temporarily, other Republicans oppose that idea, and argue that President Barack Obama should bear the blame for the loss of subsidies because he issued them to HealthCare.gov customers without the legal authority to do so.
"We have seen the difficulty that they have had in funding the Department of Homeland Security. The idea that they could agree on a way to fund the tax credits challenges credulity," Geoffrey Garin, president of Hart Research Associates, the survey firm that conducted the poll for SEIU.
King v. Burwell "creates an enormous amount of vulnerability for Republican elected officials and Republican congressional leaders to the extent they are seen as attacking and wanting to remove" the subsidies, said Garin.
"Either way, there is nothing but trouble for Republicans in this case," he said. "They are on the wrong side of public opinion."
The survey by Garin's firm is just the latest to show that while much of the public tends to see Obamacare as a whole in a negative light, individual elements of the ACA continue to be popular with the public.
Read MoreMany old Obamacare customers shopped before buying
SEIU's international executive vice president, Kirk Adams, whose union's membership includes more than 1 million health-care workers, on Monday argued that after two seasons of enrollment in Obamacare insurance, "the ACA is sort of embedded in this health-care system."
Thirty-six percent of the poll's respondents said they were Democrats, and 32 percent identified themselves as Republicans. The balance were either independent or "not sure" of their affiliation.
The poll found that 43 percent of respondents have an unfavorable view of Obamacare, with 32 percent of them having a "very unfavorable" view. A total of 36 percent of respondents viewed the ACA favorably, just 21 percent of them very favorably, according to the poll, which was conducted via landline and cellphones, and has a margin of error of 3.5 percent.