GO's operating and rehabilitation budgets are mostly covered through fares and provincial subsidies, according to the Toronto Star. Then there is a capital growth (i.e., expansion) budget, which is to be partly funded by municipalities, including a big chunk from the City of Toronto.
Expanding GO service is a bit of a mixed blessing for Toronto. There's no doubt that it helps Toronto's downtown by making it easier for people to get there from 905-land. Our downtown is certainly more successful than it might otherwise be, and as GO pointed out in a press release yesterday, this leads to higher property tax yields downtown.
On the other hand, money that goes to expand GO is money that doesn't go to expanding or improving TTC service.
On the whole, I feel that the strategic interests of the city and the cause of environmentalism are always better served by spending a dollar on the TTC instead of GO.