Greg Mankiw proposed to reduce corporate taxes in order to accelerate real economic growth, both in the short- and long-run. It is only one of many remedies proposed by macroeconomists. They do have a big problem to give not a silly recommendation based on macroeconomic analysis. But they cannot because of the inherent equilibrium state presumed by macroeconomic models. In short, this equilibrium implies that no internal force can make any change beyond the synchronized evolution of the system itself. Because these internal (economists call them endogenous) forces are well balanced they produce a very smooth growth trajectory. The only explanation of all large fluctuations around the average growth rate given by various schools of macro so far can be reduced to shocks to demand or supply, with these shocks having unknown origin. This is the feature of macroeconomics which makes it soft and worthless for quantitative forecasts. (See Krugman for the failure of the economic profession.) Economists do not really know what drives real economic growth and all their models are superficial in terms of quantities. (As a rule, economists consider the absence of empirical justification as a strong side of their theories and are proud of that. It works well before the next recession.)
The corporate taxes are external to the nature these shocks. In other words it is not shown that the change in these taxes affects real economic growth. If to neglect the theoretical impotence of this proposal (again, there is no proof that the tax reduction works in reality and will not be just waste of resources) one can make a thought experiment. Imagine that it works. Then, any reduction to the corporate taxes, as based on the macroeconomic grounds, would induce a positive feed-back and thus several iterations before these taxes fall to zero. This is simple induction – the reduction, supposedly (because there is no quantitative proof), helps – business needs lower taxes. What then? The government will need to make the taxes negative?
What to do then? According to our model, the US economy will struggle through the 2010s with the average rate of real GDP per capita growth below 2%. This implies the rate of unemployment near 9%. The slow growth will be accompanied by slight deflation. This situation has been observed in Japan since 1997 and is not too bad for the economy. The US should just be ready to redistribute the overall income in a way to support the poorest groups of population. This does not imply the corporate tax reduction any time soon.