Stimulus and the Global Coordination Problem

Matthew Yglesias' posts emphasizing the interconnectedness of the global economy and the need for coordination, like this one, are quite correct in pointing out that economies are not contained in little national boxes with policy levers nation-states can pull to goose aggregate demand, brake the rate of job loss, and so on at will. Indeed, having a sound sense of the extent of global economic interconectedness is tantamount to admitting rather hard limits on the ability of national monetary and fiscal interventions to fix things.
Suppose Matt is right when he says:

The economy is very global, and it’s extremely difficult to see it pulling short of a depression if the European Union and Japan are twiddling their thumbs. Beyond that, if there isn’t meaningful global coordination of stimulus efforts then protectionist pressures are going to become harder-and-harder to resist in China and the United States to prevent free riding. That, in turn, would buy some short-term assistance at the cost of really hobbling the prospects for recovery down the road. 

That is to say, given globalization, effective stimulus is a lot like effective carbon-reduction policy: it requires overcoming incredibly difficult international coordination problems. One might argue that the global policy coordination problem is easier to solve if the U.S. is willing to be the first mover. But then one should also admit that the domestic efficacy of American stimulus is conditional on things beyond the control of American policymakers and that the odds of success are rather lower than most progressives have so far been willing to admit.
If I were a Democratic strategist, I would, like Matt, be broadcasting the importance of global coordination in order to prepare Americans for the possibility that domestic stimulus proves ultimately impotent in the face of a broader global decline. Democrats will then be able to say “At least we tried and it would have been worse if we hadn't” in reply to Republicans keen to capitalize on the failure. If I were a Republican strategist, I would be pointing out how convenient it is for Democrats to have failed to mention the importance of perhaps unattainable global coordination when pushing through their plan. As it happens, I'm neither, so maybe I'm just concern trolling.