"The poll shows what you would intuitively think. Tea partyers and conservatives out there may cheer and more financially support taking drastic action on this but the moderate Republicans and independents and, of course, Democrats will hold Republicans responsible for the shutdown," says Kirk Jowers, the head of the University of Utah's Hinckley Institute of Politics.
"That's a very dangerous move if Republicans really are committed to expanding the tent to legitimately campaign for national office again."
Some GOP members, including Sen. Mike Lee of Utah, have argued that the Republican-led House should force Democrats to vote on a budget resolution without Obamacare funding or be responsible for failing to pass a stopgap bill that would halt nonessential government services past Sept. 30.
Lee's spokesman Brian Phillips said Thursday that the Heritage poll's numbers on who would get blamed are "meaningless."
"The government will be funded with or without Obamacare," Phillips said. "All the talk about shutdown is a way for the president, Democrats, and their allies in the media to talk about something other than rising public opposition to the health care law."
Heritage, which continues to fight against the Affordable Care Act, is headed by tea-party leader and former South Carolina Sen. Jim DeMint, a strong Lee ally. Its poll showed nearly 68 percent of poll respondents in GOP-leaning districts said it would be appropriate for Congress to temporarily halt funding for the health care law to ensure "they do not do more harm than good." Just 25 percent said they opposed such a move.
Other polls have shown little interest among Americans even those opposed to the health care law to force a government closure.
A poll by the Morning Consult newsletter recently showed 47 percent of Americans would be less likely to vote for a member of Congress who backs shutting down the government while 28 percent said they'd be more likely to support a member who does.
Heritage's poll had the opposite findings: 48 percent more likely to vote for a member who tries to slow down or halt the health care law to 25 percent who would be less likely. The difference can be chalked up to the survey sample.
"To me, it's polling at its worst," says Jowers. "[Heritage's] questions were very leading and calculating to get a result. And the representative samples were incredibly skewed. ... The poll was designed for results and not for information."
The poll included nearly 42 percent Republicans to 33 percent Democrats. Some 10 percent of the 1,000 people surveyed came from Matheson's district, though Heritage did not release results from that cross section.