It turns out, an almost 40% increase in federal tax revenues would be required.
This year's budget deficit is predicted to be $1.6 trillion. Over the next ten years, the White House projects a $9 trillion cumulative deficit, while Congress is predicting a $7 trillion cumulative deficit.
total tax receipts, including individual, corporate, excise, etc were only around $2.5 trillion in 2008. Next year, and probably in the few that follow, tax revenue should fall.
For the budget to break even over the next dedade with the same amount of spending, the increase in tax revenues needs to be 28% if revenues stay constant and the low end deficit figure is used, and 36% if revenues stay constant and the high end deficit figure is used. If tax revenues stumble, as expected, the tax increases need to be more like 40%.
Politically, this won't happen. Congress and the President will not balance the budget over the next ten years. Taxes will not be increased that much without new programs to use the revenues. But, ultimately, all spending must be paid for somehow. All public spending that doesn't itself carry with it a right to repayment (e.g. a company bailout or studnet loan) is a tax increase in the indefinite future.
The increase in the total tax burden at all level of governments to balance the aggregate government deficit would be smaller, because state and local governments generally have to have balanced budgets, and finance loans with pre-planned repayment options.