If the prices of oil continues in this direction, inflation will be a problem, Fed would hesitate to cut rates and the share market will drop. Market sentiment will be affected and recession may follow.
The FED will cut rates because #1) they are bankers and will take care of their own #2) this is an election year
Greenspan was very concerned about inflation, I think that is their central task to maintain stability in the macro economy. They aren't really bankers and hopefully they won't think of themselves as bankers. But I agree that this is an election year, the political pressure may be there.