MIAMI — As many states prepare to introduce a linchpin of the 2010 health care law — the insurance exchanges designed to make health care more affordable — a handful of others are taking the opposite tack: They are complicating enrollment efforts and limiting information about the new program.

Chief among them is Florida, where Gov. Rick Scott and the Republican-dominated Legislature have made it more difficult for Floridians to obtain the cheapest insurance rates under the exchange and to get help from specially trained outreach counselors.

Missouri and Ohio, two other states troubled by the Affordable Care Act, have also moved to undercut the law and its insurance exchanges, set to open on Oct. 1. In Georgia, the state insurance commissioner, Ralph T. Hudgens, has said he will do “everything in our power to be an obstructionist.”

Alarmed by the resistance, the secretary of health and human services, Kathleen Sebelius, and the Obama administration are intensifying their efforts to win public support for the exchanges in Florida and elsewhere and are confronting their critics head on.