TOPEKA, Kan. — Kansas’ conservative governor vetoed a bill Thursday that would have extended the state’s health coverage for the poor under former president Barack Obama’s signature health care law, setting up a likely showdown with the Legislature.

Republican Governor Sam Brownback argued that the proposed expansion of the state’s Medicaid program would fail to serve ‘‘the truly vulnerable’’ ahead of ‘‘the able-bodied,’’ and that it would burden the state budget with ‘‘unrestrainable entitlement costs.’’

When the Republican-controlled Legislature gave final approval to the measure Tuesday, it had strong bipartisan majorities in both chambers, but supporters were short of the two-thirds margins necessary to override a veto. Nevertheless, they planned to try, with a vote first in the state House as early as Monday.

Brownback has been a vocal critic of the 2010 Affordable Care Act, and his veto was expected. He previously could count on fellow GOP conservatives who opposed the former Democratic president’s policies to block a Medicaid expansion.

But voters last year turned on the governor and elected more Democrats and moderate Republicans to the Legislature, forcing a debate. Advocates for the uninsured never abandoned their push, and the Kansas Hospital Association backed an expansion, believing it could keep dozens of rural hospitals open.

‘‘Are we going to wait for some more hospitals to close?’’ said state Representative Susan Concannon, a rural central Kansas Republican. ‘‘Are going wait until we have people die that can’t get insurance?’’

Obama’s health care law encouraged states to expand their Medicaid programs by promising to pay most of the costs.

Associated Press