State governments have the power to continue what the federal government was doing and even band together. Since states will do what they want anyway, I suggest running on the 10th amendment. Enforcing the 10th amendment from the anti-federalist perspective will by itself will eliminate over 95% of the federal government. There does not need to be a power vacuum, you can just break up any agency that violates the 10th amendment into 50 parts and place them under state control.

The main thing opponents will attack you on will be fear of what will happen if a monopoly of essential services quickly shuts down operation. Outside of the "but who will pick the cotton" fear based argument I also expect you to see "united we stand divided we fall" repeated everywhere.

The first one can be dismissed by assuring every citizen that as long as their state government decides to continue to the programs it was given responsibility over, nothing will change except more self determination and less corruption.