Breaking ranks with Republican colleagues, four conservative GOP governors who preside in capitals west of the Mississippi River have decided to accept federal funds to expand Medicaid, the state-federal health care program for low-income families and the disabled.

The governors of Arizona, Nevada, New Mexico and North Dakota are on record as opposing the Affordable Care Act, the 2010 federal health bill that was the principal legislative achievement of President Obama’s first term. But as state and local costs for helping the medically uninsured rise, these governors want a share of the available federal cash.

“With this move, we will secure a federal revenue stream to cover the costs of the uninsured who already show up in our doctor’s offices and emergency rooms,” Arizona’s Jan Brewer said in explaining why she decided to accept federal funds for expanding Medicaid.

Key members of the Republican-controlled Arizona State Legislature remain to be convinced, but the governor’s spokesman said he believes that mathematics will persuade them. Arizona would receive $1.6 billion in matching funds in 2014, the first year of the expansion.

The other GOP governors who favor expanding Medicaid are Brian Sandoval of Nevada, Susana Martinez of New Mexico and Jack Dalrymple of North Dakota. All these states have rural populations in which hospitals and clinics are especially hard-pressed.

Sandoval, a practical conservative in an economically devastated state, was the first to opt for the expansion, doing so in December when all other GOP governors hewed to the party line of opposition. Sandoval is also one of the few Republican chief executives who have agreed to implement the federal law’s best known feature: creation of online marketplaces known as exchanges for individuals and families to purchase affordable health insurance.