Government spending and employment

I was browsing the web and I came across this chart released by the Federal Reserve Bank of St. Louis and the chart had compared the amount of government spending to the rate of employment and the two mirror each other. I find this even more interesting when I'd looked at the Clinton administration and the amount of spending was lowered and unemployment sank to an amazing rate. This graph is especially good for the libertarians and Anarcho-Capitalist because when government spending goes down so does employment therefore the most logical conclusion based on this chart is government spending should be at a minimum or just even decide on just abandoning it and everyone will have a job without the use or force or violence