The Greek government runs a primary budget surplus.
http://www.wsj.com/articles/greece-misses-target-on-budget-s...
Just not one large enough to satisfy creditors. That means, without the debt payments, Greece would be free and clear and wouldn't have any budget issues. The only reason Greece needs 'constant infusions of cash' is to pay off these debts, which becomes more difficult as more austerity is demanded.
Most of the recent infusions of cash were part of the ELA -- so /not/ to pay off debts but to compensate for illiquid (or insolvent...) banks and the stave off bank runs.
The debt payments are /not/ in any way big or difficult -- the EU took over most of the debt and in the process forced through a large haircut on the debt + Greece got artificially low (very low!) interest rates + enormous maturity extensions. Greece also got (much) deferred payments for that debt, especially for the interest.
But it was not a productive business, anyway.