To better understand what
deregulation means, suggest you go to
http://www.gpoaccess.gov/CFR/ and in the "Quick Search" box, type in "Health care" and see what the results are.
In the hierarchy of laws, once a bill becomes a law, the agency(ies) affected must then issue
regulations which further define how the law will be implemented and administered. The old joke is "one paragraph of statute results in 100 pages of regulation."
Deregulation involves a review of existing regulations, many of which have become obsolete, to get rid of what no longer accomplishes anything and still creates paper nobody reads anyway, as well as what is still on the books, but the statutes have changed so that the regulation doesn't describe fact. There are SO MANY regulations that are out-of-date its almost unbelievable, but they are still the law and people/organizations still are required to comply.
Also, an agency just can't delete or change a regulation. The Administrative Procedures Act governs the regulatory process to include when postings in the Federal Register must happen so that the public is aware of the agency's desire to end a regulation, why it's ending, and under what statutory authority is it being done. It's not an easy job, and the visibility and paper trail to do it is quuite long.
When politicians use scare tactics in describing
deregulation they are betting the public doesn't understand the process (which is usually true).