I'll take that bet, I can imagine several scenarios where just a few words from him/her would drive prices up or down.
Which would be a momentary blip.
The president (any president) has the same control over oil prices as he does over the stock market, which is virtually none.
Far too many mouth breathers think that there's a great big valve in the Oval office, and at a whim the President can go in and turn it to control prices.
Oil, gasoline, and heating oil are internationally traded market commodities, the prices of which are set by the actions of market traders. Yes, they can be influenced by the words of a national leader, but unless that national leader is the head of one of the heavyweight oil producing nations, the influence isn't going to be all that dramatic.