Both bills fit in with the GOP's ongoing attempt to rein in federal rules that they say are hurting domestic energy development and job creation. Republicans have approved numerous deregulation bills over the course of the 112th Congress, all of which say would help create jobs.

"The other side seems to assume that occasionally Americans are in need of daily oversight from the federal government," Rep. James Lankford (R-Okla.) said during rule debate. "That unless some federal bureaucrat or some federal regulator is not standing next to their bed when they get up, they won't know how to get to work."

The Congressional Replacement of President Obama's Energy-Restricting and Job-Limiting Offshore Drilling Plan, H.R. 6082, would replace the administration's oil and gas leasing plan, which puts new offshore lease sales off limits for five years. The bill would also require additional lease sales off Alaska's coast beyond those in Obama's current plan.

The Red Tape Reduction and Small Business Job Creation Act, H.R. 4078, would not only prevent major rules until unemployment falls, but it would also prevent President Obama from issuing last minute regulations if he loses the November election.

The White House has threatened to veto both bills, but regardless, the Senate is expected to ignore them completely.

During debate, Rep. Alcee Hastings (D-Fla.) argued that the "red tape" bill would effectively shut down major regulations indefinitely, since it's unclear when unemployment might fall to 6 percent.

"Under this legislation, federal agencies would be prohibited from issuing new regulations until the unemployment rate falls below 6 percent, and I defy any economist or anybody else in the world to tell me when that's going to be, in an economy such as the one that we have," he said.

Rep. John YarmuthJohn Allen YarmuthRyan leaves legacy of tax cuts and deficits Kentucky candidate takes heat for tweeting he'd like to use congressman for target practice Republican health policy is destroying rural health care MORE (D-Ky.) called on House members to oppose the rule because Republicans will not allow consideration of his amendment that would allow regulations to go forward if they help U.S. service members and veterans.

"Most legislation has unanticipated consequences," he said. "This legislation has a consequence that is easily anticipated, and that is that we will be tying the hands of the agencies that serve our brave men and women in the armed services."

Rep. Virginia FoxxVirginia Ann FoxxImmigration fight threatens GOP farm bill Ryan, GOP scramble to win support for controversial farm bill House to vote on farm bill with food stamps revamp next week MORE (R-N.C.) said his amendment was ruled non-germane by the House Parliamentarian, and thus could not be considered.

Just before the vote on the rule, Democrats tried a procedural move to bring up a bill prohibiting Congress from recessing until it has passed a middle-class tax relief bill. But this motion failed in a party line vote, as they always do.

After the vote, the House planned to begin work on the drilling bill, H.R. 6082, but was expected to hold a final vote on that bill Wednesday.