Honestly, the receipts for MOST businesses are fairly predictable (within 10-20%, at least), so why would we think that the government would be any different?
Also, I'm not sure why making government departments beg for money and have to live in the free market is on the face of it a bad thing. Would it be any different than the current system, where politicians beg us for money while promising to allocate our taxes a particular way, but then usually fail to follow through completely on? Having the departments beg for money directly seems more efficient somehow.
Of course, I think what would really suffer is bold new infrastructure programs. People would be willing to allocate money to roads once a couple high profile bridges collapse, but would we ever see a space elevator?