You won't find any Democrats using the phrase "Big Government" because it's a loaded, derogatory phrase. Nonetheless, the Democratic platform is generally in favor of spending on social services, like welfare, unemployment benefits, Social Security, and education, as well as generally favoring higher amounts of regulation for businesses and industries. Some of these positions are relative: keep the same amount of environmental regulations instead of reducing them, or cut education but by a smaller amount than oil subsidies. Some of them are contingent on the economic climate: avoiding cuts instead of increasing spending. But in general, yes, the Democrats do envision a larger government role in society (excepting defense/security) than Republicans do. They just don't come out and say so because that would be politically disadvantageous.