McCaul says that policy helped the U.K. dramatically reduce the amount of new regulations they imposed.

"This commonsense policy should be emulated in the United States, where the number of pages in the Code of Federal Regulation has more than doubled since 1975," McCaul said last week as he introduced his bill, H.R. 2997. "The One In, Two Out Act will force regulators to make tough choices when considering new regulatory burdens on businesses."

The bill was introduced just as House Republicans finished off a week of passing several bills aimed at limiting federal overreach. Among those bills were proposals to ensure taxpayer rights when dealing with the IRS, require all ObamaCare regulations to be approved by Congress and limit bonuses for senior government workers.

Co-sponsors of McCaul's bill said the proposal would bring more help to companies that are suffering under expanding federal rules.

"America's small businesses are strapped with too many costly regulations that don't make sense," Rep. Paul Cook (R-Calif.) said. "With our economy still struggling we should be easing regulations on small business, not adding more."

McCaul said it costs companies about $1.75 trillion to comply with federal rules each year. He said the number of new federal rules with an economic cost above $100 million has increased 60 percent in the last decade.

Other co-sponsors of the bill are Reps. Mike Conaway (R-Texas), Lynn Jenkins (R-Kan.), Randy NeugebauerRandy NeugebauerWarren’s regulatory beast is under fire – and rightfully so Dem senators to Trump: Don't tell consumer bureau chief 'you're fired' Overnight Finance: Carson, Warren battle at hearing | Rumored consumer bureau pick meets Trump | Trump takes credit for Amazon hirings | A big loss for Soros MORE (R-Texas), Steve Pearce (R-N.M.), Tom Rice (R-S.C.), Mac Thornberry (R-Texas) and Roger WilliamsRoger WilliamsGOP baseball manager gives emotional speech before delivering trophy to Scalise’s office Lawmakers celebrate National Selfie Day on Twitter Lawmakers struggle to maintain unity after shooting MORE (R-Texas).