You could now (effectively) vote for a candidate or party and through your allocation of tax dollars keep them on a leash. It would allow for a more nuanced political system. For example I might vote for a deficit reducing Republican but I don't trust them to keep their hands off the EPA so I give environmental protection 50 points. Maybe I vote for a Democrat but I still think the deficit is really important so I put 50 points on deficit reduction. This would add a whole new dimension to politics and give some power back to the people. It would in my opinion make the commons relevant again. As it stands today I think many Americans are feeling like their vote is no longer all that important. You get two choices, you vote for one or the other, pat them on the back and cross your fingers. That's just not good enough. By controlling a few hundred billion dollars of the budget we might find ourselves on equal footing with PACS, lobbyists, media tycoons, etc.
Of course there are a lot of practical details I didn't address. It may be this could only cover domestic discretionary spending, or perhaps you could only allocate your tax points every 2 or 4 years to provide for more stability and of course for long-term deficit reduction it would have questionable value since the overall level of spending/revenue would still be playing a central role.
Now, if we could vote on Congressional salaries, that might be interesting.
BTW, a friend and I also thought of this idea independently; we called it "mandatory taxes, voluntary distribution" [1]
[1] http://canadaduane.posterous.com/mandatory-taxes-voluntary-d...
In 2000, voters thought they picked "humble foreign policy", "deregulation" and "lower spending" in the primary. It turns out they voted for the exact opposite.
About 2 years ago, voters thought they picked "not forcing people to buy insurance they can't afford". They also voted for the exact opposite.