I think that's the point. Short-term borrowing is sometimes a smart idea, as long as there's a real plan to pay it off. The idea would be to only discourage irresponsible borrowing.
> This same logic, if we allow it to be applied to the deficit, could be applied to other things.
I think it's fairly uncontroversial that having unpaid debt is bad and should be avoided.. so it's not too similar to issues that are actually controversial.
There are legitimate reasons to discern between the deficit and those other things. Most law systems are based on a small set of core values which are deliberately made hard to change, i.e. made part of the supreme law.
I believe that the (preventing of) deficit has the characteristics shared by those core values: there is a consensus that it is bad (especially in the long term) and yet there's strong temptation to create it for the short term benefits (buying votes.)
The point I'm making is that everyone has a different idea of what those core values are.
The right way for anyone to figure out what their core values should be is to apply reason. Dedicated, hard-core Christians feel a certain way about a lot of things, but they ultimately base their conclusions on faith, which is the antithesis of reason.
This is basically a method of legislating a budget cap. Your 'slippery slope' argument in its correct analogy is no more than passing a law that outlaws gay marriage in the first place.