There is no hard and fast answer to the OP's question. It's a gotcha because he is hoping to challenge anyone who takes it seriously by grilling them as to why that this number instead of that number. He will never - ever - offer his own number to defend it and certainly will never offer meaningful spending cuts across the board.
My answer is this: The top 10% should pay
all of the needed* federal income tax, with some sliding scale that causes someone in the 92nd percentile to pay a little more than someone in the 91th percentile and so on, until the top 1% pay more than all those making less. The reason for that should be patently obvious. To spread the "pain" (so painful being a billionaire!

) it could be expanded to the top 20%, but no more than 25% should be paying.
Since I know some people don't see the obvious, the reasons to have the top incomes pay the taxes are that first and foremost they can afford it, that they benefit the most by far from government and that they have the power of political donations so if they think their taxes are too high, they can lobby for an actual reduction in the budget so they pay less.