The biggest problem in the US is the electorial system that leads to two parties with each close to 50%. Elections are so close that it is essentially meaningless. Is a party with 50.1% really more legitimized to rule than the one with 49.9%?
Step one to fix democracy would be to get rid of the winner-takes-all system. Not only would this make more than two parties viable. You would also fix that most of the country's vote doesn't contribute at all (since people live in "safe" counties where they have little influence on the outcome.)
Then, when elections are won with clear margins, yes, you could abolish elections, and replace them by representative polls! The benefit is that polls are much cheaper, you can do them much more frequently, and the people can change bad policy quicker. It might be controversial, but I like that you can also apply "reweighting" to polls to make them more representative.