I say the states instead of the people just based on the logistics of trying to hold an election for every issue or piece of legislation. Unless we move to some kind of vote-by-phone, secure blockchain election.

We're essentially talking about adding a third chamber to Congress, depending on whether the proposed legislation is vetoed before or after it reaches the President's desk.

Your point about the legislatures acting too quickly - they might have to slow down and think about what they're passing if they know someone else has veto power.