The cut backs in the public sector are only of course to deal with the government debt (aka National debt), which is reduced by cutting spending and/or increasing increasing taxes. But governments have tried various ways to get spending of their balance sheets - most famously privatisation in the 1980s and PFI in the 1990s (roughly).
The thing is all money is owed eventually to a bank, with interest. This is the same in the public and private sectors. There isn't enough money in existence to pay back the loans and the interest, so someone has to go bust. It's financial musical chairs as we chase money around in ever faster in cyclical consumption.
National debt is a bit of a misnomer - it should include all the money everyone owes.