I also recall one of the Peanuts characters using the phrase in comic books I was reading in the 70s.

To express the same meaning, my father, a Londoner would say 'this will either make it or break it'.

My copy of The Dinkum Dictionary (A ripper guide to Aussie English), 1988 Helen Johansen (Claremont) offers this succinct definition:

Sydney or the bush
all or nothing, complete success or total failure

The Dictionary of Australian Colloquialisms, 1985 GA Wilkes (Sydney University Press) offers a definition and several examples of usage:

1924 Truth (Melbourne Newspaper) April 6:
Sydney or the bush: All or nothing

1930 E. Shann An Economic History of Australia p365:
'Sydney or the bush!' cries the Australian when he gambles against odds, and the slogan betrays a heart turning ever towards the pleasant coastal capitals.

1945 Cecil Mann The River p45:
He bet on a Sydney or the Bush basis; and now, to-morrow, it was the Bush.

1953 T.A.G. Hungerford Riverslake p127;
'Spin for five', Murdoch suggested to Novikowsky. 'Sydney or the bush!'

1969 Mr David Fairbairn [challenging Mr Gorton for the leadership of the Liberal Party] Bulletin 15 November p27:
'Well, gentlemen, the die is cast. For me it's Sydney or the bush - Kirribilli or Woomargama.'

1970 Richard Beilby No Medals for Aphrodite p34:
'Here we go.' Turk murmured grimly, climbing in behind the wheel. 'It's Sydney or the bush! Keep your fingers crossed.'

1983 Sun (Sydney Newspaper) 30 December p39;
It's hard to pick a middle ground. The [investment] choices for next year appear to be boom or bust, Sydney or the bush.

Cheers all

aussiebloke