Some Republican lawmakers — still reveling in Tuesday’s statewide election sweep — are proposing an unprecedented solution to the state’s estimated $25 billion budget shortfall: dropping out of the federal Medicaid program.

Far-right conservatives are offering that possibility in impassioned news conferences. Moderate Republicans are studying it behind closed doors. And the party’s advisers on health care policy say it is being discussed more seriously than ever, though they admit it may be as much a huge in-your-face to Washington as anything else.

“With Obamacare mandates coming down, we have a situation where we cannot reduce benefits or change eligibility” to cut costs, said State Representative Warren Chisum, Republican of Pampa, the veteran conservative lawmaker who recently entered the race for speaker of the House. “This system is bankrupting our state,” he said. “We need to get out of it. And with the budget shortfall we’re anticipating, we may have to act this year.”

The Heritage Foundation, a conservative research organization, estimates Texas could save $60 billion from 2013 to 2019 by opting out of Medicaid and the Children’s Health Insurance Program, dropping coverage for acute care but continuing to finance long-term care services. The Texas Health and Human Services Commission, which has 3.6 million children, people with disabilities and impoverished Texans enrolled in Medicaid and CHIP, will release its own study on the effect of ending the state’s participation in the federal match program at some point between now and January.

State Representative John M. Zerwas, Republican of Simonton, an anesthesiologist who wrote the bill authorizing the health commission’s Medicaid study, said early indications were that dropping out of the program would have a tremendous financial ripple effect. Mr. Zerwas said that he was not ready to discount the idea, but that he worried about who would carry the burden of care without Medicaid’s “financial mechanism.”