I actually brought a similar idea (Mine had 100% of the funds selected) that I brought up with my wife. I'm not sure how well it would work on a national level, I was thinking of it on a state level.
I figured that while at first everything would be a mess, gradually things would even out and stabilize and the public would be able to move more quickly to fix problems and do away with wastes. At first, say everyone put all their money into one thing and the roads started to fall apart, next year they would put a lot of money into roads. Then the schools suck so they put some more money into those and gradually people even things out to close to where they are now.
My wife, correctly pointed out that unpopular programs would end up being underfunded or canned. And I said thats exactly the point! If no one sees any value in these programs, NO ONE, then why do they even exist.