MIAMI — Hospitals nationwide could lose half a billion dollars in federal funding for uninsured patients next year under the national health overhaul — a loss that will hit especially hard in states that decided against expanding Medicaid coverage. Cuts could jump to $4 billion in 2020, according to estimates released by federal health officials.

Hospitals that treat a large number of uninsured residents have relied on federal funding in the past to offset the cost. But the Affordable Care Act assumes that more residents will have Medicaid or private health insurance, meaning hospitals would see fewer uninsured patients and need less assistance.

But hospitals in states that declined to expand Medicaid — such as Florida, Texas and Pennsylvania — stand to lose the federal funding without a corresponding increase Medicaid-covered patients to offset it. The decision not to expand means potentially millions of residents in those states who would have been eligible for the expanded Medicaid coverage will continue going to the emergency room when they are sick — and hospitals will be stuck with the bill.