Given that outlays are equal to taxes when the budget is balanced, what must the US government do to balance its budget?Economically speaking
You've just said what a government in general has to do to balance a budge, so are you asking what specific steps the US government has to take in order to make its budget balance?
If so, it clearly has to A) increase revenues that it gets from taxes and/or B) decrease the amount of spending that it does. Practically speaking, the US government would have to do both in order to balance its budget because the annual deficit is so large.
As far as increasing tax revenues, most people would say that the government needs to raise taxes. However, there is also a school of thought that says that lowering taxes will increase revenues as people work harder because the lower taxes give them more incentive to earn. (See the Laffer Curve link for this theory.)
As far as lowering spending, entitlement spending is clearly the major part of the budget and so any serious attempt at balancing the budget would have to do something about entitlements. (See the usconvervatives link for a proposal.)