The waivers have been issued in the last several weeks as part of a broader strategic effort to stave off threats by some health insurers to abandon markets, drop out of the business altogether or refuse to sell certain policies.

Among those that administration officials hoped to mollify with waivers were some big insurers, some smaller employers and McDonald’s, which went so far as to warn that the regulations could force it to strip workers of existing coverage.

At a time when the midterm elections are looming and Republicans have been vocal in campaigning against the law, reaction to the rollout has been closely watched.

To date, the administration has given about 30 insurers, employers and union plans, responsible for covering about one million people, one-year waivers on the new rules that phase out annual limits on coverage for limited-benefit plans, also known as “mini-meds.” Applicants said their premiums would increase significantly, in some cases doubling or more.

These early exemptions offer the first signs of how the administration may tackle an even more difficult hurdle: the resistance from insurers and others against proposed regulations that will determine how much insurers spend on consumers’ health care versus administrative overhead, a major cornerstone of the law.

Several leading insurers, including WellPoint , Aetna and Cigna , have also objected to new rules requiring them to cover even those children who are seriously ill, warning that they will stop selling new policies in some states because the rules do not protect them from having to cover too many sick children.