The "If You Like Your Health Care, You Can Keep It Act" addresses what Johnson says was a false promise by President Obama—"If you like your plan, you can keep it" under the health-care law.
"It was totally false advertising," Johnson said in an appearance on Fox and Friends Thursday morning.
Obama's claim has taken heat recently as many individuals receive cancellation notices from their insurers. The administration maintains that cancellations were going on long before Obamacare.
Individuals are able to stay on "grandfathered plans" under the law, unless insurers significantly change them. Any new plans must offer the protections guaranteed under the Affordable Care Act.
Obama said Wednesday that individuals who were dropped from coverage can find quality plans on the health-care exchanges.
Johnson recognized that Congress wouldn't be able to allow every American to keep their plan unless the law is repealed.
His bill had 37 cosponsors as of Wednesday afternoon.
Johnson's legislation follows a similar measure introduced by House Energy and Commerce Committee Chairman Fred Upton, R-Mich., on Monday, called the "Keep Your Health Plan Act."