COLUMBUS, Ohio — As a Republican chairman of the House Budget Committee in the 1990s, John R. Kasich wielded a ferocious budget ax. On Monday, as Ohio’s governor, Mr. Kasich defied his party’s majorities in the state legislature to push through a multibillion dollar expansion of Medicaid under President Obama’s health care law.

By a 5-2 vote, an obscure committee, the Controlling Board, which normally oversees relatively small adjustments to the state budget, accepted $2.5 billion in extra Medicaid funds from the federal government. The money, recently approved by Medicaid administrators in Washington, will provide coverage for 275,000 Ohioans who have not been eligible for the program, the Kasich administration said.

The vote was an extraordinary — and possibly illegal, critics in Mr. Kasich’s own party said — end run by the governor around the General Assembly. Mr. Kasich, who initially declared himself an opponent of the Affordable Care Act and who has declined to set up a state online health insurance marketplace, has argued all year that his sense of Christian compassion, not to mention cool economic practicality, favored extending Medicaid to poor adults and those with disabilities who do not currently qualify.

But Republican majorities in both houses of the General Assembly blocked expansion. Opponents expressed disbelief that Washington would keep its promises under the health care law to pay almost all of the costs of expanding Medicaid, the joint federal-state health insurance program for the poor, and worried that Ohio taxpayers would have to pay.