EU don't seem to have a problem...
EU got better election systems and have more constrained constitutions... US complain about the Government overreach while having a Constitution which is tiny, dead (i.e. not update regularly) and is interpreted to the eyeballs by a bunch of unelected political appointments.
The US voting system is antique at this stage... One man one voting is ridiculous in this day and age... It creates two parties who can be hijacked by nature and fear of the other side..
So this 'Big Government' can be used as a fear tactic to scare people...
Independent thinker you are fearmongering that Government will take over, instead of saying, we need Government working for the citizens...
So if you see the Government actually helping you want to reject it, in fear that they could control you. You have been conditioned to live your life in fear of people you could help you...
Contrast that to Europe, Governments work for the people and they are very clear about that... The police are government workers for you, politicians are rewarded for working for the people and because the voting system, don't work for the people and you're out... There is no such thing as a safe seat for your party in most cases...
Politicians in Europe have to face the opposition once a week to answer questions... PM's can be voted out in the morning by their own party and they will do it.