But in a speech on the House floor Monday, Foxx said the federal government has found ways around these rules over the years.

"The Unfunded Mandates Information and Transparency Act will correct these oversights and put some weight behind UMRA to ensure no government body purposefully or accidentally skirts public scrutiny when jobs and scarce resources are at stake," she said.

Under her bill, H.R. 899, agencies would have to apply UMRA to all final rules. Foxx said that currently, some federal agencies avoid cost analyses by determining that a rulemaking process is not subject to a Notice of Public Rulemaking.

It would also allow judges to stay rules or invalidate them if it's found that UMRA analyses were not done.

Elsewhere, the bill would give all people affected by federal regulations a chance to weigh in on these proposals, and clarify the deadline federal agencies must meet in providing information about their rules.

"Lawmakers, the unelected regulators should know the price of their dictates," she said Monday. "So too should the people, private enterprises and governments, all of whom are being asked to foot the bill."

Cosponsors to the bill are Reps. Loretta Sanchez (D-Calif.), James Lankford (R-Okla.), Mike McIntyre (D-N.C.) and Collin Peterson (D-Minn.).