WILMINGTON, Del. — Laquita Gardner, a sales manager at a furniture rental store here, was happy to get a raise recently except for one problem. It lifted her income just enough to disqualify her and her two young sons from Medicaid, the free health insurance program for the poor.

She was relieved to find another option was available for the boys: the Children’s Health Insurance Program, known as CHIP, that covers nearly nine million children whose parents earn too much for Medicaid, but not enough to afford other coverage.

But CHIP, a program that has had unusually strong bipartisan support since it was created in 1997, is now in limbo — an unexpected victim of the partisan rancor that has stymied legislative action in Washington this year. Its federal funds ran out on Sept. 30, and Congress has not agreed on a plan to renew the roughly $14 billion a year it spends on the program.

“I’m kind of shocked, because this is something for kids,” Ms. Gardner said Thursday as her 7-year-old, Alexander, braced for a flu shot at a bright, busy neighborhood clinic run by the Nemours Children’s Health System. Ms. Gardner pays $25 a month for her sons’ CHIP coverage, with no deductible or co-payments.