More fatally for the president, the argument works. And it works precisely because of GOP extremism. If one party simply refuses to support anything a president of another party proposes and is primarily devoted to obstructionism on everything, then they can, if they are reckless enough both to create a credit crisis and prevent any further stimulus, succeed in essentially blackmailing the country by destroying its political system and then blaming it on the president. It's cynical and corrupt and contemptible and unpatriotic - but lethal.
Bingo! It also helps if they put forward a candidate willing to lie through his teeth. They've got that too.