The very term "big government" is a Reagan-era, Ayn Rand-influenced invention. No president seriously doesn't agree with the power of the presidency. Trump is using it more than any president in decades and decades. Bernie is perfectly right that the right is AT LEAST as "socialist" as the left in terms of "government intervening", it's just that it's in favor of agribusiness and big business generally. There is no genuine "small government" party except the actual Libertarian party, and you can see how popular they are. The Tea Party was SUPPOSED to be that, but as actual True Believes like Justin Amash keep pointing out - it turns out they were just waiting for an authoritarian they liked.
"Giving the government more power over us"? Please. I grew up in England, where even MARGARET FUCKING THATCHER, who made Reagan look like a wishy-washy centrist, couldn't lay one clawed talon on the cherished institutions like the NHS (ooooh! Socialized medicine!!!) and the BBC (oooh! State propaganda!), so she had to settle for destroying the unions instead. I even got a 100% free university education, as did everyone in my generation, Tory government or not. Nobody in the UK is saying "relieve me from the oppressive yoke of my free healthcare and free education!" any more than people in the US are saying that about "big government" programs like, oh, public education, Social Security, Medicare. I'd love to know what TANGIBLE freedoms we lose when we gain the very obvious freedom of "being healthy and employable" from those programs.