Or think of it this way:
City Stu in 2010: " Hello Mr Bank Manager, my business is in the shit, I'm in debt big style but I'm going to reduce my current spending and in five years time my books will balance and I can start bringing my total debt down".
Bank Manager: " Alright mate".
City Stu in 2015: "Hello Mr Bank Manager, sorry I haven't eliminated my deficit yet but it's down by 60% and falling."
Bank Manager: Too right you haven't eliminated your deficit, if you had your debt would have been 1.3tn and falling, as it is it's 1.6tn and rising. When are you going to get rid of your deficit?"
City Stu: " Er ..by about 2025....... Maybe"
Bank Manager: " You're 'avin a giraffe , by then your debt will be 2tn and if interest rates go up you'll never pay it back, especially as you're leaving that trading club. No way, you're not borrowing any more I'm capping your overdraft today. Goodbye mate".
It's a possibility, but I'd say a bigger possibility under Labour as the deficit would have been larger and therefore the debt growing faster.
That situation is essentially what's happened in Greece. Deemed irresponsible so their credit rating is shot so they literally can't borrow money so they have no choice but to spend less than they bring in in taxes. That's actual austerity rather than what we've faced in the UK (we still pay far more on public services than we take in tax).