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Mr. Kasich‘s decision is significant not only because Ohio is a political bellwether, but also because of his previous service is Congress, where as chairman of the House Budget Committee in the late 1990s he helped pass major legislation to reduce federal debt.

That gives his decision Monday added weight and could undercut arguments from some conservatives that Washington cannot be trusted to honor its financial commitments for the latest Medicaid expansion.

Ohio was among 26 states that sued to overturn the federal law. The U.S. Supreme Court upheld the heart of the overhaul last year but allowed states to decide whether to expand Medicaid.

Mr. Kasich joined Arizona Republican Gov. Jan Brewer in calling for expansion. Several other GOP governors have said they will not go forward, including Gov. Rick Perry in Texas, Bobby Jindal in Louisiana and Nikki Haley in South Carolina.

The Medicaid expansion is intended to cover about half of the 30 million uninsured people expected to eventually gain coverage under the health care overhaul. The law expanded Medicaid to cover low-income people making up to 138 percent of the federal poverty level, or about $15,400 a year for an individual. That provision mainly will benefit low-income adults who do not have children and currently can’t get Medicaid in most states. Separately, the overhaul provides subsidized private insurance for middle-class households.

The District of Columbia and 17 states have opted to expand their Medicaid rolls.

• Associated Press writers John Seewer in Toledo, Ohio, and Ricardo-Alonso-Zaldivar in Washington contributed to this article.