People may define the term in many different ways, but how it's actually used by everybody used boils down to one thing --
"Big government" is "government that does things I don't approve of".
And the opposite is of course "small government" -- "government that doesn't do things I don't approve of".
The Republicans say that the Democrats are the party of "big government", but the Republicans want to limit what we can do in the bedroom, they want a huge military, they're worried about which bathrooms we use ... who's the party of "big government" again?
The Democrats say that the Republicans are the party of "big government", but the Democrats want socialized healthcare, to keep God out of our schools, to open our borders, to have massive welfare programs ... who's the party of "big government" again?