About 27 percent of people under 65 are thought to have some sort of pre-existing condition that will most likely leave them without individual insurance if the law is repealed, according to a recent study. The guarantee of coverage has already become a rallying cry for people who want to keep the law.

The issue “is the third rail” for the Republicans, said Michael Turpin, a longtime health industry executive.

Before the law, a fairly typical life event — like a divorce or the loss of a job — and a relatively minor medical condition could upend a person’s health coverage options. Stories of sick people unable to get coverage when they needed it most were legion.

Mr. Trump insists he wants to keep the pre-existing requirement for insurers, and other top Republicans say people who want coverage should not be turned away. Details about how they will cover people with existing medical conditions have not yet emerged, but many lawmakers have started pushing an idea — known as high-risk pools — that left many people uncovered or with strict limits to their coverage in the past.

The challenge for lawmakers is this: How do you get insurers to cover people who will definitely need costly medical care — and do so without making insurance too expensive for everyone?