It wasn't the Progressive Era that brought a big increase in federal spending as a percentage of GDP. It was WWI. In fact, by this metric spending generally declined from 1900 to 1916.
Found a neat chart. Don't know how to post it directly.
http://www.alhambrapartners.com/wp-content/uploads/2012/05/Ritholtz-spending-to-GDP-052812.png
Good image and a good find. Sure looks like a post-Civil War “Fedzilla” to me ;’)
Look more carefully, you'll notice that Federal spending was already rising before WWI, and never went back to that 3% level afterwards.
Republican spending in the 1920s was generally that 3% plus national debt payments, but the Great Depression made both Republicans and Democrats crazy, and so spending rose to 5% and then 10% even before Second World War spending kicked in.
After WWII, Eisenhower set Federal spending around 15%, of which 10% or more was military, but ever since, military has fallen (about 3% today) and non-military risen to over 20% of GDP.
But again, my point is: Southerners loved "Big Government" under their Democrat heroes like Wilson and FDR, and even voted for Adlai Stevenson in the 1950s, before finally figuring out that Liberal Democrats really weren't so interested in them...