Michael Mandelbaum sees a cash-strapped America as dangerous for the world:
Here the impact of the coming economic constraints on foreign policy will differ from the effects of the downsizing of the financial industry. Reducing the size of banks and other financial institutions will have benign consequences, reducing the risk of a major economic collapse, limiting economically unproductive speculation, and diverting talented people to other, more useful, work. By contrast, the contraction of the scope of American foreign policy will have the opposite effect because the American international role is vital for global peace and prosperity. The American military presence around the world helps to support the global economy. American military deployments in Europe and East Asia help to keep order in regions populated by countries that are economically important and militarily powerful. The armed forces of the United States are crucial in checking ambition of the radical government of Iran to dominate the oil-rich Middle East. For these reasons, the retreat of the United States risks making the world poorer and less secure, which means that the consequences of the economically-induced contraction of American foreign policy are all too likely to be anything but benign.
Mandelbaum skips over the context of those military deployments: the Cold War. But luckily for us, it's over. The consequences of an American military withdrawal from Europe is significantly less risky for the world in 2010 than it would have been during the Cold War. Second, in some regions of the world that are volatile, such as the Middle East, the U.S. military is arguably doing more harm than good. Large scale military deployments to keep the peace in the Persian Gulf after ousting Saddam from Kuwait only catalyzed a worldwide terrorist movement against the U.S. and ultimately drew the U.S. into a second, more costly, war in the region that did huge harm to the U.S. economy with no commensurate benefits. A similar gambit aimed at containing Iran may not end much better.
The exception to this dynamic, I would argue, would be Asia, where the U.S. does face a potential challenge in China - a country that could do serious harm to American economic interests (although shows no signs of doing so at the moment). But there's no reason to fear "down-sizing" in America's foreign policy if it's done in a manner that moves American forces from where they're no longer needed to ensure they can afford to stay where they are required.
The bigger danger is that policymakers will refuse to try to make considered cuts and adjustments. They will try to "do more with less" instead of "doing less with less."