A simple cross sectional plot of recent data on debt and social expenditures as a % of GDP for OECD countries suggests some positive correlation. Two caveats are in order. First, if you look at total government expenditures what you find is in fact a negative correlation. Second, the optimal size of a welfare state or government is not determined by whether it has a large deficit.
Tim Vlandas 
Where is this data from?
This data is taken from the OECD statistic website, which can be accessed at: http://stats.oecd.org/Index.aspx