Actually, cutting the deficit in half is wildly improbable. In addition to the various expenditures discussed, the Medicare and Social Security trust funds are in transition from surplus (which means the total federal deficit is reduced) to deficit (which means an additional deficit added to the existing problem).
KEY DATES FOR THE TRUST FUNDS (HI is Medicare's Hospital Insurance fund)
First year outgo for HI exceeds income excluding interest 2008
First year outgo exceeds income including interest 2010
Year trust funds are exhausted 2019
Notice that 2010 is a key date. So either taxes must increase, Medicare benefits must be reduced - or some other portion of the budget must be slashed still more deeply.
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Perhaps a better analogy would have the hapless student chained to the floor of the pool as a flood of debt fills it. However, it is still possible to scoop water up in the bucket and sling it elsewhere within the pool. It won't do any good, but it makes quite a show...for a time.