The bill also strips the U.S. Supreme Court of any appellate jurisdiction over these issues.
"Last week, President Obama made an unprecedented decision to declare a federal law unconstitutional and thereby abdicate his own constitutional responsibility to uphold and defend that law," Burton said. "Activist judges, and now an activist president, have been trying to unilaterally define marriage for too long. This issue should instead be decided once and for all by the American people and the states."
Republicans in recent days have sharply criticized the administration's decision not to enforce the law. Rep. Blake Farenthold (R-Texas) on Thursday called the decision a violation of the separation of powers principle in the Constitution, and Rep. Dan Lungren (R-Calif.) warned of oversight activities in the House.
Lungren is a member of the House Judiciary Committee, which as of Friday morning had not scheduled a hearing on the issue or a markup of Burton's bill.
Co-sponsors of Burton's bill are Reps. Todd Akin (R-Mo.), Rodney Alexander (R-La.), Roscoe Bartlett (R-Md.), Joe Barton (R-Texas), Jeb Hensarling (R-Texas), Ralph Hall (R-Texas), Walter Jones (R-N.C.), Jim Jordan (R-Ohio), Doug Lamborn (R-Colo.), Bob Latta (R-Ohio), Ron Paul (R-Texas), Dennis Ross (R-Fla.) and Joe Wilson (R-S.C.).