Initially it would probably be a mess. But I also think more involvement is the only way to build a more responsible, informed, interested citizenry. People need to feel that they can affect things, that they have a say in policies.

I think a lot of people are indifferent because it doesn't seem to matter whether they vote for the red or blue team every few years, <insert favorite cause> doesn't seem to be improving. If they had a slider to set their preferred allocation of public spending and they could vote on specific proposals about <their favorite cause>, they would probably be more inclined to participate and do so in a more responsible manner.

You can't force people to participate though. Maybe you could optionally delegate your vote, and then it would be effectively the same level of involvement as with the current hands-off representative system. But at least you could still withdraw or reassign the voting power at any time.