Mr. Strack isn’t alone in his concern. As the American population ages and insurers try to rein in costs, the share of health and medical costs that retirees can expect to shoulder is becoming more formidable.

A look at estimates of retiree health costs suggests that, if long-term care costs are included, it is not difficult to come up with a situation in which a couple’s tab for out-of-pocket costs post-retirement could approach — or even exceed — $1 million.

Getting to such a large number can mean combining some bleak possibilities — say, both spouses ending up in a nursing home in a high-cost part of the country — and factoring in extended life spans. But it is not far-fetched.

“It’s certainly possible,” said Paul Fronstin, a researcher at the nonprofit Employee Benefit Research Institute.

That doesn’t mean it is likely for most people. But it does suggest that most need to think about saving a lot more for health costs in retirement. Half of Medicare beneficiaries have below $77,500 in personal savings, according to the nonprofit Medicare Rights Center.