"This White House and this Congress is demonizing them — the new drilling moratorium, the new energy taxes — all of that is costing us tens of thousands of jobs in the middle of what's supposed to be a recovery, but it's a very poor one," he said.

Republicans have complained that the administration's energy policies — such as the six-month moratorium on new offshore deepwater drilling operations following the Gulf of Mexico oil spill — are costing jobs in the energy industry. GOP leaders have also ridiculed the administration's energy and climate proposals as a tax on energy.

But Republicans have also been prone to missteps that have allowed Democrats to frame the GOP as being forgiving to the oil industry.

Rep. Joe Barton (R-Texas), the top GOP member of the committee overseeing energy policy, famously apologized to BP CEO Tony Hayward when Hayward testified on Capitol Hill about his company's handling of the oil spill.

Barton called the Obama administration's efforts to force BP to create a $20 billion recovery fund for Gulf Coast residents a "shakedown" — a political gaffe that resulted in the House GOP leadership leaning on Barton to apologize, along with several calls from Republicans for Barton to step down from the plum committee position.

The June apology has become a central part of Democrats' election-year messaging — the Democratic National Committee has created a website labeling some GOP incumbents and candidates as "BP Republicans."

Brady said Republicans are simply interested in creating energy jobs.

"We think American energy jobs are good and we ought to encourage more of it," he said.

More broadly, Brady argued that the economy would benefit from GOP victories this fall.

"You're not going to be hearing a lot of this anti-job proposals, the tax increases, the increased energy prices," he explained. "I think everyone realizes that we're going to have a healthier economic climate with Republicans holding control of the House."