No. (Of course, it would require a constitutional amendment to make this happen.) Of course, what you are really asking is whether we should have a referendum on everything the government does. I can't think of the last major law that was passed by the federal government that I supported. At the same time, I guess you are asking whether a "pure" democracy would or could work. Is there reason to believe that the simple majority is "right?" I have neighbors who own houses who don't know the first thing about international relations or government economics or much of anything the government does. They also have no knowledge of history, or the constitution. Nothing wrong with them, their interest lie elsewhere. (Football, as it turns out, nothing wrong with that either.) But, much as I like them as people, I am not sure that they would be competent to vote on government spending. I am not sure that I am competent to vote on government spending. I don't think that there have been many of our representatives who are really competent to discuss government spending. Politicians are experts at getting elected.
I would have loved to vote down hundreds of things our government has done over the past few decades, Winston Churchill is quoted as saying, "It has been said that democracy is the worst form of government except all the others that have been tried." I am not sure that going to a system where uninformed and incompetent voters overthrow uninformed and incompetent elected officials would be any better than just letting the elected officials maintain the current system.