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The announcement was a surprise even to journalists who were provided an advance copy of Mrs. Brewer’s speech — minus the section on the Medicaid expansion. Mrs. Brewer said as recently as last week she would make a decision soon, but didn’t hint it would come in the State of the State address.

Seventeen states and Washington, D.C., have now signed onto the expansion, and nine have opted out. The rest are weighing the decision.

Overall, the Medicaid expansion accounts for about half the 30 million uninsured people expected to eventually gain coverage under Mr. Obama’s 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 a single person. That provision will mainly benefit low-income childless adults, who currently can’t get Medicaid in most states. Separately, the overhaul provides subsidized private insurance for middle-class households.

Under the legislation, Washington would pay the entire cost of the Medicaid expansion for the first three years, gradually phasing down to 90 percent of the cost after that. It’s a far more generous matching rate than the federal government provides for other parts of the Medicaid program.

Mrs. Brewer told lawmakers that expanding Medicaid would help poor Arizonans and help hospitals and caregivers who now must give care without pay. An estimated 300,000 more Arizonans would be eligible for the state’s version of Medicaid under the full expansion.

Republican state Rep. John Kavanagh, an opponent of expanding Medicaid, said he doubted the governor’s plan will clear the Legislature.

“The Legislature doesn’t like Obamacare, and this is a critical part of it,” he said.