Polls tend to show that a plurality of voters disapprove of Obamacare, but that they would rather see lawmakers carve out an alternative solution to the law than force a government shutdown to defund it.
The findings have left lawmakers on both sides of the aisle claiming momentum in the high-profile battle this week over whether to block funding for Obamacare before it starts to take hold next week.
"If the issue is about the president's health care plan, then given the country's attitude, that should be a favorable exchange for Republicans," said David Winston, a GOP pollster. "But if the issue is whether the government is going to shut down or not, then that completely changes the context."
Mr. Winston said polls show the legislative battle is playing out against a backdrop of growing voter frustration with the inability of elected leaders in Washington to carve out solutions to the problems they face in their daily lives.
"People are now looking at Washington and saying, 'When are you going to start fixing things,'" he said.
The GOP-controlled House approved a stopgap spending bill last week that would keep the government funded and included a provision that would block funding for the Affordable Care Act.
The Democrat-led Senate is scheduled to tackle the issue this week and is expected to restore funding for Obamacare — setting the stage for another House vote, which will determine whether the federal government stays open beyond the fiscal year, which ends Monday.
The ongoing stalemate coincides with a new survey from the United Technologies/National Journal Congressional Connection that found that 63 percent of Americans think that lawmakers should approve funding for government operations and to deal with the health care law separately. That is compared with 27 percent who say lawmakers should fund the government only if President Obama agrees to delay or withdraw his signature domestic achievement.
A CNBC All-America Economic Survey released earlier this week painted a similar picture, with 59 percent of the respondents saying they oppose defunding the law if it leads to a government shutdown.
But voters generally disapprove of the law.
A Pew Research Center poll released last week that showed more Americans disapprove than approve of the law by a 53 percent to 42 percent margin.
The Pew poll also found that the opponents of the law are split over what they want Congress to do now that the law is beginning to take effect.
More than half of them said that lawmakers should do what they can to make the law work as well as possible. Slightly fewer said Congress should do whatever is in their power to kill the law.
Republican pollster John McLaughlin said that the popularity of the health care law has been on a steady decline and that the party could strengthen its hand if it rolled out a plan that combined the popular parts of Obamacare — including allowing people to remain on their parents' health care plan until age 26 — with the ability to buy insurance across state lines and medical malpractice reform.
"We could put out a popular plan to replace Obamacare, but the defund battle seems to be getting in the way of forcing Democrats to vote on what could be a better plan," Mr. McLaughlin said.
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