Obviously, if Hillary runs and wins, she increases her chances...if she runs and loses, she decreases her chances...
NY is a blue state, so any generic D is favored over any generic R. Yes, Lazio did run poorly, but it had been thought that Giuliani would be the nominee.
In short, I do not expect Hillary to back down.
If she runs and loses, she's toast. It's all over.
How can she possibly beat a Republican in a general election if she can't even beat a Republican in a Democrat stronghold?