The US sort of does have referendums already, with people voting on various "propositions" during elections.
Direct democracy is kind of stupid though when you think about it. You elect leaders to lead, you're hiring them for their expertise. It's like going to the doctor for treatment and then after examining you she asks you what form of treatment you should take. If your doctor is worth the price, she should know better than you what to do.
The real problem is that people keep going back to the same two doctors. They get treatment from one that doesn't work so they go to the other one, and that doesn't work either, so instead of going to a third doctor, they go back to the first, and when that doesn't work they go to the second one again, it's insanity. You know what I'm talking about.
The only thing direct democracy is good for is deciding controversial but essentially unimportant issues like *** marriage. It's a way for politicians to avoid having to make those controversial decisions and have to defend them for the rest of their careers.
When it comes to making important policy decisions, a good leader should be better equipped to make the right choice than the average person.