There are too many factors:
1) The scope of the game
2) The visuals of a game
3) The engine for the game
4) The complexities of bringing said game to the market
Each one can adversely effect the budget. It really depends on what your looking for. A HD "blockbuster" will cost around $20-25m in "most" cases, and expects to sell no less than 1m units to be profitable. There are many scaled back ventures from that kind of investment.
And having said that, a key factor is your staffing - If you have a good staff (or a cheap staff), you can get away with some very good things.
Example: Gears of War vs. Red Steel.
Both games cost the EXACT same amount of money. Guess which one looked better and sold more? It's weird to think that Gears of War only cost $10m to bring to the market, but indeed it did. Why? Epic made UE3, and was incredibly familiar with the process of bringing a game to fruition on the system, so much of the assets were already there, just waiting to be transformed into an uber-game.
And budgets don't always determine success. Braid was made for XBLA on a budget of around $500,000 including everything, and made it's entire budget back in around 2 weeks....And has turned Jonathan Blow into a millionare in a matter of weeks. It's all about taking advantage of what you can on the system of your choice: I am sure that the makers of Game Party and Carnival Games are very excited about the price vs. performance of those 2 said games.
Back from the dead, I'm afraid.
