"Necessary" revenues?

In the ongoing "fiscal cliff" negotiations (read: public gamesmanship; there have been no actual negotiations yet) to avoid the expiring tax rates and automatic budget cuts previously enacted by Congress, the White House has created an arbitrary requirement for a certain amount of revenue that it says it must reach for any meaningful proposal. From a response to Jake Tapper in the White House press briefing today:

"[We] have not seen and no outside independent economist has seen a credible proposal that says you can achieve the kind of — the kind of revenues that are necessary for a balanced approach just by closing loopholes or capping deductions."

Who decided what amount of revenues are "necessary" for a "balanced approach"? One might think he means (and a good approach would be) the revenue necessary when combined with complimentary spending cuts to reduce the deficit to $0 and balance the budget. However, the total amounts we're talking about in any potential deal are literally fractions of the annual deficit. President Obama's proposal is $2 trillion, Speaker Boehner's proposal is $2.2 trillion, Bowles-Simpson is $4 trillion, but these are all spread over 10 years, where the deficit every year has been over $1 trillion for each of the last four years. So what is this unspecified target that the amount of new revenue must reach? Assuming the White House likes their own proposal and thinks it is itself "balanced" and meets the targets "necessary", this appears to be roughly 1/5 of the annual deficit. Why is that the proper goal? Why not 1/4 of the deficit? Why not 1/2? Why not the whole thing?

The Obama proposal includes $1.4 trillion in revenue from tax increases and $600 billion from spending cuts. Given the White House's reliance on the "balanced approach" trope, are we to assume that they think the numbers 1,400 and 600 are somehow balanced? Do they even know the meaning of the word? Actually, the House proposal of $800 billion in revenue (from deduction elimination, not rate increases) and $1.4 trillion in cuts is numerically more balanced than the White House proposal. However, in the real world neither of these proposals is actually balanced or even comes close to repairing the enormous fiscal damage done over the last six years.

UPDATE: During the budget/debt ceiling talks in 2011, President Obama suggested that $1.2 trillion in tax revenue could be raised by elimination deductions and credits without raising rates (or even with lowering them). Why isn't that possible anymore? And assuming he thought $1.2 trillion was a "balanced" amount of revenue then, why is $1.4 trillion balanced now and $800 billion not?