Gov. Rick Perry of Texas, who also turned down the Medicaid money and is thought to be considering a second presidential run, used even more vivid language. “It’s like putting 1,000 more people on the Titanic when you knew what was going to happen,” he said.

He also said in an interview between sessions of the Republican Governors Association meeting that it would matter in a political context.

“I think it’s a factor; I think it’s a philosophical position,” Mr. Perry said of Medicaid expansion, noting that even President Obama had called Medicaid — which is financed by both the states and federal government — part of “a broken system.”…

Gov. John Kasich of Ohio expressed this political fact of life, becoming animated as he was questioned at a meeting with reporters here about his decision to expand Medicaid.

“I always try to put myself in the shoes of somebody else to say: ‘How would I feel if I didn’t have health insurance? Are you kidding me?’ ” said Mr. Kasich, who has been mentioned as a 2016 hopeful, his voice rising. In defending Medicaid, he spoke at length about the scourge of drug addiction and challenges faced by those with mental illnesses.