Sessions: GOP's jobs program is cutting back Dem programs

"We are going to stop the outrageous spending," he said. "We are going to attack the rules and regulations which are killing not only business but losing jobs all across this country."

Sessions added that one example of a bill that would save jobs is the GOP legislation to repeal last year's healthcare law, a move that he said would save 800,000 jobs. Rep. Rob Andrews (D-NJ) rejected that assertion, and said the U.S. has added 1 million private-sector jobs since the healthcare law was passed.

Sessions dismissed that. "We're not going to let the Democrats get us off our game," he said. He also said that while Democrats say they can accept budget cuts, they routinely reject specific proposals.

"Everything is a sacred cow," he said. "Everything that we do is a problem if you go and touch it."