A recent study by the IMF looked at 173 attempts to bring growth in the face of an economic downturn through austerity over the last 30 years. The result? Austerity under these conditions does not produce growth, reduces wages, and increases long term unemployment.
Given that this strategy always fails, why would Republicans pursue it? Possibly it's just a tool to undermine Social Security and other welfare state measures, which are very much hated by some conservative politicians and their backers.