Where I stand - on tax fairness and equality

I try to be fair in my dealings with others and at least in theory fairness should not be subject to interpretation.  However, throughout my life I have learned that is not always the case; and though we may ask for fairness and/or equality, what we actually want is accommodation.

Let's look at taxes, the federal budget and the deficit.
The latest budget submitted by Obama to congress shows a requested expenditure of 3.8 trillion dollars (that is $3,800,000,000,000).  Per the latest information I was able to find, there are 225.7 million Americans 18 years of age or older (225,700,000).
That means that if every American age 18 or older paid $16,836.51 that budget could be balanced.  (currently it is estimated that there will be over a trillion dollar deficit)
So to be "fair", all Americans would pay the same amount of taxes and if we made the bogey $16,836.51, the budget could be balanced.

But here is where it gets tricky.  Some Americans will not make that much money next year.  Others may make more, but have living expenses that will consume most of what they make or at least enough that they could not afford to pay that much in taxes.
So is "fairness" or "equality" what we want here?  I don't think either the far left or the far right (nor anyone in the middle) is asking for that (at least not that I have heard).
Instead, I hear some people saying that anyone that makes more money then them should have their tax rates increased and I hear others saying that those who are paying less taxes than they are should have their taxes increased.  Both say doing so would make things more "fair".  Both cannot be right.

It could be perceived that to be "fair" everyone would pay the same percentage of their income in the form of a tax, regardless of how much they earned or how they earned it.  But that would mean that people who didn't earn any money wouldn't pay any taxes and that would not be "fair".  So it stands to reason that it would not be possible to create a tax system that would be completely "fair".

Where then do we draw the line?  Anyone making more money than me should pay whatever taxes it would require to balance the budget and anyone making as much or less than me should have their taxes frozen or reduced?  Clearly, that would not be fair.