There is a federal law on the books from 1986, the EMTALA act
(Emergency Medical Treatment & Labor Act (EMTALA))

In 1986, Congress enacted the Emergency Medical Treatment & Labor Act (EMTALA) to ensure public access to emergency services regardless of ability to pay. Section 1867 of the Social Security Act imposes specific obligations on Medicare-participating hospitals that offer emergency services to provide a medical screening examination (MSE) when a request is made for examination or treatment for an emergency medical condition (EMC), including active labor, regardless of an individual's ability to pay. Hospitals are then required to provide stabilizing treatment for patients with EMCs. If a hospital is unable to stabilize a patient within its capability, or if the patient requests, an appropriate transfer should be implemented.

The law includes shielding doctors from prosecution if they perform an abortion to save the life of the mother. Federal law trumps state law in every case.

TikTok video about it.