To Krugman, the fundamental problem is currently spare capacity in the US economy. This has been caused by a rise in private sector saving (both by firms and consumers). He argues, that given the liquidity trap we face, extra stimulus is needed to boost growth. He argues that in a liquidity trap, the extra borrowing is unlikely to cause a rise in interest rates, but, would help stimulate economic growth and enable improved finances over the long term. Despite the experience of Greece, Krugman makes the point, that rising government borrowing has not caused a rise in bond yields. But, bond yields have actually fallen - showing that critics of stimulus have exaggerated the fear of rising bond yields. (The Hawks who cried wolf)
Mankiw makes an argument that increasing stimulus now, would be less effective in boosting demand because of the fear of future higher taxes would discourage higher spending.
If the government borrowed the money to spend, it would need to eventually pay the money back. That means higher future taxes, on top of the future tax increases that President Obama already will need to impose to finance his spending plans. Higher future taxes reduce demand today for at least a couple reasons. First, there are Ricardian effects to the extent that consumers take future taxes into account when calculating their permanent income. Second, those future taxes are not likely to be lump-sum but will be distortionary; it is plausible that at least some of those future tax distortions may adversely affect the incentive to invest today. (Mankiw)So Who is Right?
I have always been sceptical of this argument of Ricardian equivalence that taxpayers look at stimulus packages and save in anticipation of tax rises years later. If done at the proper time, stimulus packages can restore confidence and boost growth, when it is most needed. It is this return to growth that can help improve the cyclical budget deficit.
Mankiw expresses a strong sentiment in American politics which is an extreme dislike to any idea of rising taxes.
On bond yields, it is true that higher borrowing has not caused bond yields to rise. But, this does not mean it will always be like this. The experience in Europe shows that bond markets can quite quickly lose patience and require higher bond yields. But, the other interesting thing is that bond markets often fear negative growth and deflation as much as planned increases in borrowing. A stimulus package that increased growth and avoided deflation would help long term prospects for American debt - probably more than austerity packages that threatened a double dip recession.
Another issue is that the deficit is complicated by the fact there is a mixture of cyclical factors and long term structural problems (rising health care costs e.t.c). However, you can't solve structural problems by ignoring cyclical problems.