THE BURNED OVER DISTRICT

And it is that daily closer contact with the voters of their states that pushes a more practical approach to Medicaid on Republican governors that their more ideologically hidebound senators and congressmen can choose to ignore.

A week later, his state’s Republican governor, Dennis Daugaard, announced that he wanted to make 55,000 additional South Dakota residents eligible for Medicaid under the law.

“I know many South Dakotans are skeptical about expanding Medicaid, and I share some of those sentiments,” Mr. Daugaard said. “It bothers me that some people who can work will become more dependent on government.”

“But,” Mr. Daugaard said, “we also have to remember those who would benefit, such as the single mother of three who simply cannot work enough hours to exceed the poverty line for her family.”

In state after state, a gulf is opening between Republican governors willing to expand Medicaid coverage through the Affordable Care Act and Republican members of Congress convinced the law is collapsing and determined to help it fail. In recent months, insurers have increased premiums and deductibles for many policies sold online, and a dozen nonprofit insurance co-ops are shutting down, forcing consumers to seek other coverage.

But in Arizona, Arkansas, Indiana, Iowa, Michigan, New Jersey, Nevada and Ohio, Republican governors have expanded Medicaid under the health care law or defended past expansions. In South Dakota, Tennessee and Utah, Republican governors are pressing for wider Medicaid coverage. And Republican governors in a few other states, including Alabama, have indicated that they are looking anew at their options after rejecting the idea in the past.

That has created tension with Washington that some lawmakers can no longer ignore.

“I am very reluctant to take positions that counter the decisions made by the governor,” said Senator John McCain, Republican of Arizona, where more than 78,000 people have gained Medicaid coverage under legislation signed in 2013 by Jan Brewer, a Republican who was then the governor. Now, Gov. Doug Ducey, also a Republican, is seeking a federal waiver to charge premiums and co-payments and create work incentives within the limits allowed by federal rules.

“The governor and Legislature in my state decided that they wanted” to expand Medicaid, Mr. McCain said.

Joan C. Alker, a senior researcher at the Health Policy Institute of Georgetown University, said the divide was “a reflection of the larger fight in the Republican Party between more pragmatic Republicans, including governors, and the ideological wing of the party that wants to stop Obamacare at all costs.”

Tarren Bragdon, the chief executive of the conservative Foundation for Government Accountability, said that to governors of both parties, federal funds looked like “free money.” By contrast, he said, Republicans in Congress focus on costs to the federal government and believe that the expansion of Medicaid will not be sustainable or affordable in the long term.

And so ACA drives a wedge between Republicans and allows their voters to see the malicious contradictions in Teabagger ideology.