Barbour was quoted in a Huffington Post article:
"This administration's policies have been designed to drive up the cost of energy in the name of reducing pollution, in the name of making very expensive alternative fuels more economically competitive," said Barbour in a speech to the U.S. Chamber of Commerce in Washington, DC
I'm not sure if this goes anywhere from here. The recent spike in oil prices has been caused by conflict in the Middle East. The Obama Administration has always taken great pains to frame their policies in encouraging alternative energy research and expanding public transportation as designed to ween the United States off of its dependence on Middle Eastern Oil. Barbour's accusations don't hold much water.
The more I think about it, the more I wonder where these alternative fuels that Barbour claims Obama is trying to push are. As far as I have seen, Obama has been compromising to use traditional fuels in more environmentally friendly ways. The White House has been a verbal proponent of clean coal power and exploration and cars with better fuel economy - policies that should drive down the cost of energy, not increase it.
I fail to see what political gain the Obama Administration would have for driving up the price of oil. Even if you oppose their policies, it isn't wise to assume that the administration is stupid.
Barbour claiming that Obama is purposely driving up the price of oil is like me claiming that Barbour caused Hurricane Katrina to hit his state in 2005 - purely ludicrous.