In reality we don't need any miners. There are 7 million bitcoins in existence which is probably more than half what will ever get generated (early adopters who mined and thought the whole thing to be pointless and deleted their wallet, hard drive crashes, stolen and reformatted computers, deceased bitcoin owners not informing anyone of their wallet, etc). More than enough bitcoins out there to satisfy speculators.
Except for the fact that the security of the existing bitcoins is directly related to the difficulty level. The mining part isn't there to distribute bitcoins, it's there to keep them safe.