I definitely wouldn't argue it might work to that single ended goal (reducing the deficit). Although much like any half-cocked law it has 'unforeseen' ramifications and collateral damage.
Legislation takes time to have an effect on the economy.
If our deficit starts to increase, we recognize it, then take action... how will we know if it's enough? How will congress know it's enough to protect their jobs or so far overboard it will increase the wealthy/poor divide? What if the deficit lull was just a blip on the radar? Once action is taken, how long until it corrects the problem? What if the solution takes ten years?
If a law like that was passed our Government will simply keep the decicit as negative as possible. This results in a massive divide between the wealthy and poor. You will have to purchase your house outright, your income will decrease, jobs will decrease, etc. The wealthy no longer answer to the poor yada yada yada. For a nice case study on this check out Soviet block states.
Something more productive would be for society to EXACTLY define government's role. Should government only defend from outside invaders, increase productivity with roads/bridges/water treatment, how about regulating how homes are constructed, or what is considered 'goat cheese' vs 'goat/milk blend'?
A well drawn line around your goal makes it easier to focus on.
#2 and #3 are problems within problems and too abstract to discuss on this simple forum.