Neither major political party legitimately wants a small government.
Republicans being the party of "small government" is debatable. They support unlimited military and law enforcement spending. They support the expansion of the prison industrial complex. The expansion of the police state. Strong federal restrictions on immigration. They support the government regulating people's bodies, what goes on in people's bedrooms, how you're allowed to express your gender, what you're allowed to teach, etc. Even if you restrict the concept of a small government to just the economy, they have no problem with huge bailouts for corporations when the free market eventually crashes. Red states use more federal funding than blue states. "Small government" is just a slogan with no actual substance. Republicans are simply against the government preventing them from doing what they want, while being completely fine with the government doing stuff to other people. They're only "small government" when it comes to the government doing anything to protect workers or working class people, and the IRS staying out of their business when they're doing white collar crimes.
They're just as much of hypocrites as so many Democrats who act like they're the party of the working class, while working at the behest of corporations, and any sort of reform to our system to benefit workers is seen as "too radical", and they even conspire against the thought.