According to the Wall Stree Journal tick-tock, President Obama told John Boehner that the road in which they don't reach a fiscal-cliff agreement features "a spike in interest rates and a global recession." As Paul Krugman argues, and Brad DeLong follows with even more detail, this is an extremely unlikely particular case of the general myth of the bond vigilantes.
Now, that said, I wouldn't draw any broad conclusions about Obama's view of macroeconomics from the fact that two Wall Street Journal reporters say that someone reliable said that Obama said this to Boehner. The reporters may be misunderstanding. Their source may be lying. Obama may have been lying to Boehner. Shit happens. But still it's more troubling than if we had an account of the president giving a brilliant and accurate description of the basic economics of the situation. Krugman says that possible confusion here "has real-world consequences" because this belief-set would make Obama "too eager to reach a deal now now now, and hence too willing to concede on fundamental priorities."
Even that's not totally clear to me. The interest rate spike story just seems incoherent. Suppose investors do start dumping treasury bonds and interest rates rise. Where does the money go?
Well it could go into private domestic investments, which would boost the economy. Or it go into foreign financial assets, which would reduce the value of the dollar and boost the economy by bolstering exporting and import-competing firms. Higher interest rates have historically caused recessions because the Federal Reserve was deliberately using high interest rates as a tool for inducing recessions because they thought higher unemployment would quash worker demands for higher wages and keep inflation under control. An exogenous reduction in the global investment community's inclination to hold treasury bonds could reduce American doctors' ability to take that trip to Paris they've been dreaming of this spring, but couldn't induce a recession.
Yet that's not to say that the fiscal cliff couldn't induce a recession. The Congressional Budget Office thinks that very rapid deficit reduction will have exactly that effect. But if going over the cliff does cause a recession, it'll drive interest rates lower by reducing inflation expectations (CBO thinks going over the cliff will drive core PCE inflation well below the Fed's 2 percent target) and demand for private investments.