The Obama administration is dialing up the pressure on a handful of states that have resisted expanding Medicaid coverage for their low-income residents under the federal health care overhaul.

The leverage comes from a little-known federal fund that helps states and hospitals recoup some of the cost of caring for uninsured patients. The administration says states can just expand Medicaid, as the health care law provides, and then they wouldn’t need as much extra help with costs for the uninsured.

Two top targets so far are Florida and Texas, with large numbers of uninsured residents. Both have received several billion dollars in recent years from Washington under the so-called low income pool, also known as LIP.

Florida’s hospital funding is the first of the nine states — which include Tennessee, California, Massachusetts, Arizona, Hawaii, Kansas and New Mexico — to expire on June 30. But the hospital funds are an optional program, not entitlement programs like Medicaid, meaning the federal government has broad discretion whether to grant them, experts say.

“There’s no doubt that other states that haven’t expanded Medicaid are watching this,” said Joan Alker, Alker, executive director of the Georgetown University Center for Children and Families.