The public isn't very knowledgable about fiscal policy and doesn't have a firm understanding of debt as it relates to the federal government. As such, it's not a surprise to learn that the public has a contradictory view on the debt ceiling. According to the latest Washington Post-ABC News poll, 71 percent of Americans say that the U.S economy would suffer serious harm if Congress fails to lift the debt limit. Even still, 51 percent of Americans oppose a deal to lift the debt limit, even if it includes spending cuts.
This is incoherent, but understandable. There are two basic positions in the public conversation over the debt limit. Republicans are against raising the debt limit, calling it irresponsible, and Democrats support raising the debt limit and predict a catastrophe if we don't. Most Americans aren't equipped to evaluate either claim, and so we get these results, where it looks as if respondants split the difference between both positions, with partisanship explaining the variance between Democratic and Republican opinions.