Who would get blamed for an economic downturn resulting from the debt ceiling standoff? John Sides, a political scientist at George Washington University, has argued that incumbents tend to get blamed by voters for bad economic conditions even under divided government. New York Times blogger Nate Silver responds that a debt-induced crisis "would not be a normal case":
Whatever else the 2012 election would be if the debt limit is not raised in a timely fashion, it would not be a normal case. There’s no especially appropriate precedent for the economy tanking by such an immediate and direct result of action (or inaction) in Washington. One reason the public tends to score strong economic performance in favor of the president, and poor economic performance against him, is because the United States economy is incredibly complicated — it’s hard for the public to discern cause and effect...
This would be different, however. The stock market could drop by thousands of points. Some major corporations, particularly in the financial services sector, might go under. Although the consequences might take some time to filter through the broader economy, there would nevertheless be a number of immediate and extremely visible effects. Many voters would feel as though they had perfectly reasonable grounds to connect the dots.
You’d have to weigh two things against each other: the additional damage to the economy, which is bad for the president all else being equal, and the additional ownership of the economy that Republicans would take for it, which is bad for them all else being equal. I don’t know which effect would win out, but it’s not a risk that either side should feel happy about taking.
It's certainly true that the current standoff seems relatively unprecedented, but as Jonathan Bernstein (another political scientist) notes, "There's always going to be some slightly new twist to almost any political phenomenon, and in most cases the new twists are a lot less important than the similarities." Over the years, people have come up with lots of stories about why the president won't get credit for a good economy or why the opposition will be blamed for a bad economy, but things rarely work out that way.
In this case, it's worth thinking through the mechanics of how Republicans would be blamed instead of Obama. As Silver notes, the economy is incredibly complex. Even if there were a debt default, the process by which it would affect the economy would be difficult for people to understand. Both sides would no doubt blame each other for the outcome and create elaborate stories about why the other side is to blame, which would then be reinforced and amplified in the press. Then more than a year would elapse before November 2012, and both sides would continue to blame each other for failing to adequately address the consequences of the default. In the meantime, many people will forget the details of what happened, but will know that Obama is the president and the economy is in bad shape. Under those conditions, how likely is it that people who would normally blame Obama for the poor economy will instead blame the GOP when they show up at the polls? Presidential forecasting and approval models aren't perfect, but I think the burden of proof is on their critics to explain why we should expect a deviation from the normal pattern of economic voting.