The now-ubiquitous Republican notion that reducing spending during an economic crisis with rock-bottom interest rates could increase short-term economic growth is not quite a lunatic notion. But it's pretty close, and it has virtually zero serious intellectual support, reports Neil Irwin:

As Republican leaders urge a steep and swift reduction in government spending, they are making an un­or­tho­dox argument: that these cuts would strengthen economic growth not only in the distant future but almost immediately.
That view is at odds with many of the nonpartisan groups that analyze the economy. Research departments of leading banks and agencies such as the Federal Reserveand the Congressional Budget Office warn that deep cuts would come at the cost of weaker growth and fewer new jobs in the months ahead, as less public money is pumped into the economy.

Irwin does say that one study, by Alberto Alesina, suggests that deficit reduction can increase growth. The study has been widely cited by conservatives. But Noah Kristula-Green shows that, in context, it does nothing to advance the case it's being used to bolster:

Alesina has indeed found cases where reducing spending was followed by economic growth and reduced deficits. The problem: he found very few cases. More specifically he found 9 examples out of 107 attempts to reduce spending.
Even if we are more generous with our parameters, the data is still not an overwhelming majority. If we are only interested in times where reducing spending was followed by an economic expansion, the result is 26 cases. If we are interested in the number of times that reduced spending was followed by successfully reducing the deficit (doesn’t mean the economy had to grow!) we find 21 cases in his data.
Chad Stone, Chief Economist of the Center on Budget and Policy Priorities, very generously went through the study to provide the above numbers to FrumForum. The following are the six countries that have seen a reduction in spending followed by both economic growth and a reduction in the deficit, with the years noting when the policies were enacted:
Finland (1998)
Ireland (2000)
Netherlands (1996)
New Zealand (1993, 1994)
Norway (1979, 1980, 1996)
Sweden (2004)
A question for any policy maker then becomes: is America in 2011 in the same situation that the Netherlands, Norway, Sweden, or any of the other high-tax European or Scandinavian countries are in? Are any of their economic situations that led to those spending cuts being followed by lower deficits and higher growth anything like the situation America is currently in?
But perhaps more immediately problematic for conservatives is that when the IMF looked at these arguments they found that growth and deficit reduction occurred in countries where cuts in spending were accompanied with easing and looser monetary policy from central banks. This means those countries also had policies such as the conservative-derided quantitative easing (QE2). (The IMF’s report states: “it appears that the difference in monetary policy responses accounts for much, though probably not all, of the difference in output performance.”)

So, to recap, there are three huge problems here. The paper has only 9 out of 107 cases that seem to support its claim. None of them are countries with similar levels of government spending as the United States. And all those cases rely on stimulative monetary to compensate for tighter fiscal policy, something that's nearly impossible at this point, and which Republicans would vigorously oppose anyway.

In short, the proposition that cutting spending will increase short-term economic growth is totally unserious. The one piece of alleged ballast turns out not to support the case.