Government with the consent of the people is how our Republic was intended to work.
No Step On Snek.
They then go into congress and do the bidding of the lobbyists, and do just enough for the "people" so as not to get tarred and feathered.
Our "states" have a say via the senate, but our senators are beholden to the lobbyists as well. Also, our states are beholden to the federal budget as many state programs are funded by federal money.
So whatever the US was supposed to be is so far from what it currently is, that arguing over fine points like "democracy vs. republic" is just nitpicking.