Believe it or not, the US has no mechanism for a national election. While the Federal Government sets guidelines for elections, each state runs its own. Every election is on the state level. Even the Presidential Election, thanks to the Electoral College, is really just a weighted sum of the outcome of 50 state elections (and DC).

Even Constitutional Amendments go through a state-by-state ratification process.

I think it’s impossible to do any sort of true nationwide referendum without a Constitutional Amendment happening first. Remember that the Constitution explicitly states that any powers not explicitly given to the Federal Government are reserved for the States (and the People). So the power to have Federal referendums would need to be explicitly granted.