When I first thought about writing this post I had not realized that the issue had been so addressed by many and that the answers were, as usual in economics, contradictory. While, like most debates in either economics or politics, it appears to be a clash of ideologies rather than pure policy or economic issues, all economists do at least agree on a simple point: deficits matter, if the sovereign nation does not issue its own currency. Recent experience from the Eurozone has shown this to be correct (any person who believes this does not hold should have a look at Greece, Cyprus, Spain, Portugal and Italy). The real debate now becomes whether deficits matter in countries which can print their own money.
The supposed prevailing view amongst Modern Monetary Theorists, as perceived by Paul Krugman, is that deficits don't matter. MMTs argue that this is not their viewpoint, as they believe that deficits do not matter with regards just to sovereign insolvency. Strangely enough, they both have some part of the truth, but not the whole.
The point with deficits is that they increase demand in any market. Just like any other economic aspect, when demand rises prices follow. This means that inflation also rises and this creates incentives for more investment and additional growth. Then, as we have all learned, the sum of a country's deficits minus the payments she already makes, consist her national debt. Under this scenario, Krugman puts forth as simple model where the government borrows from the public in one period and repays in the following by imposing taxes and issuing money. Now, according to Krugman's model, since the price level is, by assumption, proportional to the level of money in the economy, this tells us that the higher the debt burden, the higher the required rate of inflation.
Thus, Krugman concludes, there is a maximum amount of debt an economy can sustain and thus even if a country is printing her own money, deficits may cause a crisis. The first caveat in this model is that we cannot know the level of debt the economy can sustain. Japan's debt-to-GDP ratio has reached 211% in 2012, much greater than the 90% cut-off of Reinhart and Rogoff negative growth territory, and yet inflation has been on the fall over the past 15 years despite deficit spending since 1991 (see graphs below).
The (implicit) point made by Krugman is not really in contrast to the (implicit) points made by MMT proponents. Deficits can cause crises, but only if they are high enough and sustained for a long period of time, with other constraints holding the economy from growing (such as the case of the Weimar Republic or Zimbabwe). As experience has shown, hyperinflation is not just the outcome of monetary policy, although it does make for a large part of it. Hyperinflation is the simultaneous large increase in money supply in addition to a large productivity shock (discussed here). This is what happened to both the Weimar Republic when France took over its main industrial region, the Ruhr area, after WWI and what happened in Zimbabwe when land reforms caused the destruction of nearly half of the country's domestic food production. In addition both countries spent a significant amount of money to resources other than re-building the economy such as reparations in the Weimar Republic and political favours and food imports in the case of Zimbabwe. (Other deficit myths can also be found here)
Having said that, the case between Krugman (or Keynesians in general perhaps) and MMTs becomes just a case of misunderstanding each other and nothing more. Even Keynesians would agree that deficit spending is not a problem in a liquidity trap (although the question of the extent of the problem in a country not able to print its own money has not been explored yet), they believe that inflation-wise problems might occur if we are not in one. As already argued, deficit spending in times of trouble is essentially the same as the Keynesian stimulus Krugman et al have been arguing about over the past couple of years. Thus, both are in agreement here.
Yet, what would the point of increased deficit spending be if the economy is not facing trouble? I do not really think that either of the two sides would argue that increased spending in times of prosperity is not a good thing. The UK experience after WWII has indicated that a full capacity increased spending does more harm than good. In fact, an MMT proponent in the US, John Kenneth Galbairth, pursued policies by which he managed the debt-to-GDP to decline, not because the numerator decreased but because the denominator was increased.
Thus the simple conclusion is that deficits, in a country with the ability to print her own money, matter only if they are (very) large and sustained for a long period of time. Yet, the deficits on their own cannot really cause the crisis. If a country faces large and sustained deficits, then a large productivity shock could threaten the nation's solvency. Consequently, and as stated at the beginning of this post, both schools hold just part of the truth: MMT should not pose that deficits are not important for insolvency, as large and sustained deficits pose the potential danger that an exogenous shock could escalate and Keynesians should not claim that increased deficits pose direct danger for hyperinflations since this does not hold in an economy with a money-printing facility.