Most of them. Not that they actually implement small government when they get into office, but they'll scream it from the rooftops because to the "small town folks," small government equates to turning a blind eye to social justice issues. Cutting spending is never eliminating waste from government, because they'd never think of cutting the military budget. They always specifically target social services due to Reagan's welfare queen mythology that exists to this day.
Reagan wasn't "small government" either, by the way. He expanded the government faster than any other POTUS in history outside of world wars. His economic policies also gave both parties the green light to spend like it's going out of style, although Republicans are notably bad when it comes to actually making economic sense with their taxes versus their expenditures.