“It needs to be the principal message; you can’t dilute the attack by all the other stuff Trump talks about every day,” said Ed Rollins, a veteran Republican strategist.

For Mrs. Clinton, the problems with the Affordable Care Act could force a reckoning that she had hoped to avoid. As a candidate, she has linked herself more closely to Mr. Obama than any nominee has done with a sitting president in modern times, defending his economic record and praising him for pushing the health law through a sharply divided Congress.

Republicans had hoped that their nominee would force Mrs. Clinton to own the health care law, politically speaking, or at least be forced to defend it, but she has mostly skated past its flaws in cost and coverage. A Kaiser Family Foundation poll in September found that roughly six in 10 adults said the candidates’ plans to address of cost of their health insurance premiums and deductibles would be very important to their vote for president.

Still, parts of the health law are politically popular. The United States has the lowest percentage of uninsured citizens in its history. Because of the Affordable Care Act, insurers cannot deny coverage for a pre-existing medical condition and cannot cap lifetime coverage. Children can remain on their parents’ policies until age 26.

Mrs. Clinton says she wants to improve the law by increasing the subsidies that help cover premiums and allowing more Americans to receive government help.

She also wants to add a government-run insurance option, which she says would increase competition and choice in the marketplaces created under the health law. And she has proposed allowing people younger than 65 to buy in to Medicare.