They agree on the major problems in the health-care system – the high cost of care and patchwork access to insurance. But surveys also show a large rift over solutions, which suggests that both Democrats and Republicans will have to tread carefully in fashioning a policy response after a high-court ruling expected next week.
Many court-watchers believe the Supreme Court is poised to strike down a central plank in the Affordable Care Act – a mandate that individual Americans must carry health insurance or pay a fine. The court could rule that this "individual mandate" is an unconstitutional power grab by Washington against the rights of individuals and state policymakers.
Polling several months ago by Gallup found that Americans essentially expect that outcome, with fully 72 percent saying the individual mandate is unconstitutional.
No matter how the court rules, a stepped-up policy debate over health care will become part of the backdrop for the presidential election campaign.
If the court upholds the entire law or most of it, Republicans in Congress are expected to mount an effort to repeal it. Repeal is also a campaign pledge of Mitt Romney, the presumptive Republican nominee for president.
If the court strikes the whole law down, Mr. Obama and Democrats may call it an "activist" ruling that deprives Americans of provisions they largely support, such as the call for insurance companies to offer coverage to all comers regardless of their medical condition.
As the two parties prepare to argue over the law, the court ruling, and next policy steps, the public appears skeptical of both sides.
First, the law passed by a Democratic Congress and signed by Obama in 2010 isn't widely popular. Some 47 percent of Americans say they oppose the Affordable Care Act, according to a mid-June poll released this week by the Associated Press and GfK. Only 33 percent say they support it, and the support level hasn't been above 45 percent in AP polling over more than two years.
Separately, a February Gallup poll found Americans more likely to say that the law will make their own health-care situation worse rather than better.
But polls also don't give Republicans much comfort on the health-care issue.
Gallup polling in 2011 found 50 percent of Americans saying it's government's responsibility to make sure all Americans have health coverage, versus 46 percent who opposed that premise. Moving toward universal coverage, via a mix of private and government insurance programs, is the central goal of Obama's reforms.
Many Americans support the law's requirement that insurers offer coverage to consumers regardless of their health condition. Since that provision imposes extra costs on insurers, it is married in the law with the individual mandate – intended to prod millions of young and healthy people to become a new source of revenue for health insurers.
Even as many Americans say they don't like the Obama law, many would also be disappointed if it were repealed by Congress.
A new poll from the Pew Research Center finds that 48 percent of Americans would be unhappy if the Supreme Court rules the entire law unconstitutional, while 44 percent would be happy.
But a slightly larger share of Americans, 51 percent, say they'd be unhappy if the court leaves the whole law in place.
A mixed ruling, with the individual mandate thrown out but the rest of the law kept in place, would have its own public-relations challenge. Many Democrats would be disappointed, while many Republicans would wish the court had gone further. In all, 51 percent in the Pew poll said they'd be unhappy with that outcome.
What's clearest about public opinion may be this: In their concern about issues of access and rising costs, Americans don't want Washington to do nothing. If the court strikes down the whole Affordable Care Act, fully 77 percent of Americans in the new AP/GfK poll said Congress should start on a new bill, not leave the health-care system as it is.
Republicans including Mr. Romney are talking not just about repealing the act, but also about replacing it with what they say would be more effective and affordable reform.