The Keynesian Model is not a Big Government or Small Government Model, by David Henderson http://econlog.econlib.org/archives/2016/05/the_keynesian_m_1.html
If the government raises taxes during booms and lowers them during busts, or decreases government spending during booms and reduces government spending during busts, there is no built-in growth of government from following the policy implications of the Keynesian model.
If you could convince me that it [the Keynesian model] worked in a technical sense, I'd immediately favor tax cuts in recessions and tax increases in booms