As I explored briefly in my column on the politics of gas prices this is less straightforward than it might first appear. As Michael Levi writes we've traditionally wanted to distinguish between supply shocks and demand shocks as drivers of price spikes. When oil gets expensive because of a supply disruption, that hurts America. But when oil gets expensive because there's lots of demand and economic growth, that's just a sign of growth. But perhaps this time it's different. The US isn't as big a slice of the global demand pie and "western economies can be on their knees, but oil demand can still be on the upswing due to healthy growth in China, India, and other emerging economies (not least those that also export oil)."
I still think one needs to say more about exactly what the dynamics are. If China grows fast, then not only should Chinese imports of oil go up, China ought to be importing more airplanes and soybean oil and Friends reruns. Similarly if Kuwait gets rich selling oil, then we're the ones who sell them the military equipment and Friends reruns they buy. For things to go wrong for the U.S. economy something else has to go wrong over and above the oil. We can see what those "somethings" might be, related to exchange rate issues or the failure of the US government to issue a quantity of bonds commensurate to global demand. But it looks to me as if a demand-side oil issue is really just the same old issue of the trade deficit and the international balance of payments and not the second coming of a 1970s-style oil price shock. Perhaps it's a monetary policy issue. We send dollars abroad in exchange for oil, but then the dollars get sent back in exchange for bonds. That ought to lower interest rates and induce investment in the United States, but nominal interest rates are already at zero so the loop is cut. Even so, higher gas prices should push the price level up which pushes real interest rates down which induces investment in the United States. The chain will only be broken here if the Fed decides to ignore its own self-guidance and target headline inflation instead of core inflation. If you do what the ECB does and react to an increase in the price of oil imports with tighter money, then clearly higher oil prices slow growth. But that's the ECB blundering (a specialty in Frankfurt) not oil prices strangling growth per se.
Still I'm going to file this under "provisional." Apologies for noodling in public. My hope is that in the future people can spell out in more detail exactly how they think things can go wrong.