As Republicans plot strategy on Obamacare, a key disagreement keeps arising in GOP circles as the party debates whether to leverage the specter of a government shutdown in an attempt to force President Obama to abandon his signature health care overhaul: Who would voters blame for a government shutdown?

Would they fault the Republicans for being the first to threaten to withhold their critical votes for a spending bill to keep the government running beyond the Sept. 30 end of fiscal 2013, unless Democrats agree to defund the Affordable Care Act, which is already on the books?

Or would they blame Obama and congressional Democrats for refusing to support short-term spending legislation to keep the government operating after fiscal 2013 expires, just because it does not include funding for the Affordable Care Act, which remains unpopular?

While it’s possible that voters would eventually blame Obama for rebuffing a Republican proposal to delay further implementation of a law many Americans either don’t like or are wary of, polls suggest that that is not the position they hold as the debate kicks into high gear.

First, let’s examine a poll conducted June 2-5, several weeks before a small group of congressional Republicans proposed their defund-or-shutdown strategy. The survey, conducted for the Republican nonprofit Crossroads GPS by GOP polling firm North Star Opinion Research, examined voter attitudes toward Obamacare and its implementation.

Not surprisingly, the results were almost uniformly negative for Obama and other supporters of the Affordable Care Act — with the key exception being the response to this question: “Some say that the health care reform law is so bad that an effort to repeal it should be attached to a bill necessary to keep the government running. Do you think it is a good idea or a bad idea for opponents of the health care reform law to risk shutting down the government in an effort to get rid of the law?”

Only 29 percent of respondents said this was a good idea, compared with 64 percent who said it was a bad idea and 7 percent who didn’t know. The poll, which surveyed 1,000 registered voters, had a 3.1 error margin, and included the following partisan breakdown: 43 percent identified as independent-leaning Democrats on up to strong Democrats; 34 percent identified similarly as Republicans and 17 percent were independents.

Crossroads notes that, throughout its poll, only on this issue do self-described independent voters side with Democrats, a majority of whom generally support Obamacare.

Republican pollster Brock McCleary, of Harper Polling, notes the political risk in assuming that, since a majority of all voters give Obamacare a thumbs down, they are likely to live with a government shutdown if that’s what it takes to stop the law.

“It’s a big leap of faith to say that means a shutdown is an electoral winner,” McCleary said. “That thinking presumes to know the consequences of a shutdown.”

A July 30 poll sponsored by the Tea Party Patriots, which supports the defund-or-shutdown strategy, reports similar bad news for Obamacare’s popularity — as well as similarly revealing the challenge of pursuing that tactic. The Washington Examiner reported on this in depth on Tuesday.

But it’s worth reviewing additional information from the poll, which was conducted by the GOP firm GEB International. Of those polled, 50 percent supported delaying the employer mandate to provide health insurance — a move Obama announced in July — and 59 percent backed a delay in the individual mandate to obtain insurance, which is still set to go into effect in January.

According to the poll, 58 percent of the 50 percent who favor a delay in the employer mandate, and 55 percent of the 59 percent who favor a delay in the individual mandate, would blame Obama over the Republicans in any government shutdown that arose because the president declined to acquiesce to GOP demands to delay implementation of the law.

The numbers hardly show a majority of voters who currently would hold the president responsible for any government shutdown that occurs because of a disagreement over Obamacare funding, let alone one that is impenetrable. However, the proponents of defund-or-shutdown are undaunted.

“What the Democrats are saying, what the president is saying is they are willing to shut down the government unless it funds Obamacare,” Sen. Marco Rubio, R-Fla., said during an interview with conservative talk radio host Mark Levin. “And, I think that is a completely unreasonable position and one that when outlined to the American people, they are not going to support.”