Wrong. Fascism does not require a bigger federal government, in fact a larger government is generally the opposite of fascism. Fascism requires more power in the hands of fewer people.
Ah, I see the source of the misunderstanding here; it's quite a common problem when conservatives talk to liberals: you use the same words, but to mean different things. When GP talks about a "big government", he means a government that is big in terms of the scope of its powers and responsibilities. It's not a matter of headcount, which is how you seem to be using the term.
An absolute monarchy can be a "big" government if the monarch feels he is entitled to micro-manage the daily lives of his subjects. Or it can be a "small" government, if the monarch just lets people be. Likewise, a vast bureaucracy that does very little could be considered a "small" government, albeit a very inefficient one.
Sure, in practice, more power in the hands of government usually means more government employees required to deal with enforcement and administration, but the "size" of the government (to the right, who are usually the ones talking about it) is a philosophical point, not a practical one. So in those terms, a fascist government is by definition "big".
Incidentally, President Obama made the same mistake in his first inauguration address - he said something like "it's not about big government or small government, it's about a government that's the right size to help its citizens"; neatly missing the fact that big government v small government is about whether the government is there to "help" people, or just there to administer justice and provide national defence and basic public infrastructure.