The point isn’t that Ben Bernanke would deliberately set out to undermine a fiscal stimulus. He might well want Congress to enact one because it would make his own life easier: The more Congress stimulates the economy, the less he would need to engage in the types of monetary easing that have brought him so much criticism. So long as he maintains his inflation target, fiscal stimulus cannot do much to boost the economy. If the Fed adopted a nominal-income target instead, as some economists counsel, the fiscal-policy story would be the same: More fiscal stimulus would mean a tighter (or less loose) monetary policy, and the economy would end up in roughly the same place.
The dominance of monetary over fiscal policy is one reason conservatives are right to insist that we can tackle the budget deficit now without weakening the economy. If Congress cut its deficit spending so much that inflation expectations dropped below what the Fed deemed acceptable, the Fed would respond by loosening money. To the extent the market expects this response, the Fed would not even have to take much action, since inflation expectations would have a floor under them. The net result should be the same amount of economic activity, but with more of it taking place in the private sector. Many conservatives believe there would even be more economic activity. On this argument reduced spending, now and in the future, will reduce future tax burdens and thereby improve present incentives to work, save, and invest.