The thing with a tax for basic income (as opposed to other taxes) is that the money doesn't go to the government, it goes directly to the people. The government cannot decide how this money is spent, so it's not a "fat government" thing.
And what is this "past experience" you refer to? If you are referring to communism, this is in some sense the very opposite of an unconditional basic income - unconditional means the government cannot tell you what to do (nor can employers, as long as you don't want to own a car, have a nice home, etc.). Yes, "fix the economy". But how? Basic income is actually a proposal how to fix it, I think.
And what is this "past experience" you refer to? If you are referring to communism, this is in some sense the very opposite of an unconditional basic income - unconditional means the government cannot tell you what to do (nor can employers, as long as you don't want to own a car, have a nice home, etc.). Yes, "fix the economy". But how? Basic income is actually a proposal how to fix it, I think.