That definition isn't what it is in the US, at least in the common parlance/political mudslinging arena.
Liberal as a put-down here generally means something akin to "increase tax rates, and give free handouts to the poor through welfare programs. Increase the nanny state to new never seen before levels, don't let people run their own lives because we know best".
Now, does it really mean that? Probably not
But, that's generally what the "other side" would like people to think.
Conservative has generally in the past matched what you said above, but only in perceived definition - not actual actions. I think the past 8+ years should disprove that theory quite well.
In short, we have absolutely no major party in the US who espouses "live and let live". AKA "Get the living fuck out of my goddamned business, and I will give you the same courtesy in return". If we had such a party, I'd certainly vote for it and actually give a shit about politics again.
The US has moved far from it's days of folks valuing their independence, I really don't think a party following your definition of liberal would go very far this day in age here. Which is pretty sad if you ask me.
-Phil