Nine percent of companies said they expect to stop offering coverage to their workers in the next one to three years, the Wall Street Journal reported. Around 81 percent said they would continue providing benefits and 10 percent said they weren't sure.

The companies, though, said a lot will depend on how future provisions of the law unfold, since most of the key parts are scheduled to take effect in 2014. One in three respondents said they could stop offering coverage if the law requires them to provide more generous benefits than they do now, if a tax on high-cost plans takes effect in 2018 as scheduled or if they decide it would be cheaper for them to pay the penalty for not providing insurance.

While small business don't face fines for failing to offer coverage, companies with 50 or more full time employees face a penalty starting at $2,000 per worker.

Deloitte conducted the study between February and April — before the Supreme Court upheld most of the law — and surveyed corporate and human-resources executives from 560 companies currently offering benefits.