Most of the uninsured have to wait five months for the next chance to seek coverage on the health care overhaul’s public exchanges. But that doesn’t mean they need to spend the summer worrying about their lack of protection from large medical bills.

The state-based exchanges, a cornerstone in the overhaul’s push to expand insurance coverage, still permit customers to buy coverage under certain circumstances. The uninsured also can buy a temporary plan to cover them for a few months.