Leading Texas Republicans on Monday asked the Obama administration for greater flexibility to administer Medicaid — a move that has gotten little traction in the past — while reiterating that they would not participate in an expansion of the program under the Affordable Care Act.

“Any expansion of Medicaid in Texas is simply not worth discussing,” state Sen.Charles Schwertner, R-Georgetown, chairman of the Senate Committee on Health and Human Services, said at a press conference.

Schwertner and Lt. Gov. Dan Patrick both told reporters that the federal-state health insurance program for the poor and disabled was on an “unsustainable trajectory” of growing costs. In a letter, they asked the federal government for more wiggle room to administer the program, requesting cost-cutting changes to its benefits packages and seeking to require that Medicaid beneficiaries have or seek employment to get health coverage.

Similar requests by former Gov. Rick Perry for flexibility in spending Medicaid dollars failed under both Democratic and Republican presidents. About 4.1 million Texans are on Medicaid, which constitutes about 29 percent of the total state budget.

In 2008, Perry asked health officials under President George W. Bush for a waiver allowing the state to limit its number of Medicaid beneficiaries and create a less generous benefits plan. That request was rejected.

And in 2011, Perry signed legislation asking the feds for a Medicaid block grant, a capped amount of money that would have come with more flexibility for the state to toy around with spending. That proposal also hit a dead end.

Asked about previous attempts to get federal permission to change the state’s Medicaid program had failed, Schwertner acknowledged that those requests went unapproved.

“The federal government has been very unwilling to work with increased flexibility,” he said. “That’s why we are calling for increased flexibility to preserve the Medicaid program.”

State Rep. Garnet Coleman, D-Houston, said Monday that the proposals were “a nonstarter and everyone knows it.”

“We should be following the example of other Republican states who are finding fiscally responsible solutions to closing the coverage gap rather than increasing it,” Coleman said in a statement.

Twenty-eight states and the District of Columbia have expanded Medicaid under the federal law.