Influence? Yes, to a very small degree. Control? No way. If you like, I can rip apart the first several paragraphs of the author, a guy named "American View," who's biography isn't exactly one that engenders authoritative confidence in his statements. He was a NYC firefighter for 15 years before moving to Plano, TX (practically right next door to Hurst, TX), where he now enjoys woodworking, creating furniture, restoring & refinishing furniture, restoring all types of Antiques. But more important than his lack of authority in his speaking, his facts are extremely selective, skewed, incomplete, and in some cases flat out wrong.
For one, at the time Obama and his energy secretary were alleged to have said it (it was Gingrich who said it, tho), it wasn't $5 a gallon like in Europe, it was $9-$10 like in Europe. Energy Secretary Chu, way before 2008, way before he was energy secretary, way before Obama had run his first primary campaign, had made a comment in a speech that if the price of gasoline were boosted it would encourage fuel conservation. Well, duh. But somehow that got translated to Obama's Energy Secretary said that. But he didn't. Newt did.
Secondly, he's completely misrepresented what happened to fuel prices during Bush's tenure, parroting the party spin instead of presenting cold hard facts. He states that despite numerous natural disasters in the gulf, Florida coastline, wars in the Middle East, the price of gas remained stable overall during the Bush presidency. That alone should make you quit reading his stuff, because he's got the memory retention and recall of a rewritable CD that's been in the microwave for 5 seconds.
So, Mr. American View has his basic facts wrong, and he's using "common knowledge" in the place of actual facts, and presenting them as facts, because he believes them to be facts. Except that if he'd done some research, he'd know they aren't facts.
Politicians, both Republican and Democrat, since the 1970s have been rattling chains about wanting the price of gas here in the US to match that of Europe, and they want to raise taxes to do it. The problem is, Europeans pay taxes at the pump for stuff which we pay separately, things like federal excise taxes. Federal excise taxes are hidden "event" taxes which we don't pay for separately, but are included in the price of goods just the same. They are "event" taxes which are paid when something happens, like at the time of purchase for liquor, wine, cigarettes, airline tickets, land lines, sports fishing equipment, tires, trucks, gas guzzler cars (any car with an EPA rating of 22.5 MPG or less), and all the popular vaccines, and are paid by the manufacturer or retailer, and that cost is build into the price to the consumer. What a lot of politicians want to do is just raise fuel taxes and not touch excise taxes. But if they eliminated federal excise taxes today, right now, and then slapped those onto fuel prices, we'd be paying, ta-da! $9-$10 for gas, same as the Europeans. In Europe they don't have all those separate excise taxes (other than a VAT on imported goods) and everything is handled easy peasy at the pumps. If you don't buy gas, you don't pay a lot of taxes over there.
If you remove all the taxes from gasoline, including the event excise taxes, and then do the same in Europe, then the price of gas at the pump would be the same in both places, which is the world spot market price of gas.