PHOENIX — After losing on the floor of Legislature, 36 Republican lawmakers are now asking a judge to invalidate the Medicaid expansion plan they couldn’t block politically.

The lawsuit filed Thursday in Maricopa County Superior Court against Gov. Jan Brewer contends the levy on hospitals that she pushed lawmakers to approve to fund the expansion is a new tax or fee, which the challengers say requires a two-thirds vote — something it did not get.

Christina Sandefur, the attorney for the Goldwater Institute, which is representing the legislators, said they have a right to sue because each of them voted against expansion.

Further, she said, they constitute more than a third of both the House and Senate — a sufficient margin to deny the measure the two-thirds vote they contend it required.

“But because the governor signed the bill into law even though they did not have a two-thirds supermajority in either house, basically those legislators’ votes were, in effect, nullified,’’ Sandefur said.

If the argument about a two-thirds vote falters, the legislators have a fallback position. They contend the measure unconstitutionally gives Tom Betlach, head of the state’s Medicaid program, too much power to decide who has to pay the levy and how much. Betlach even exempted some hospitals from having to pay anything at all.

Under normal circumstances, it would be the hospitals that would sue, as they are the ones being assessed.

But Sandefur said the hospitals have a financial interest in not overturning the levy. In fact, Betlach structured it so every hospital chain in the state being assessed will actually benefit financially.

Figures from the Arizona Health Care Cost Containment System, the state’s Medicaid program, estimate hospitals will shell out about $75 million for the first six months of 2014. But AHCCCS estimates that, in total, they will get back $108 million more than that over the same period.

The key is that the legislation, coupled with federal dollars, will provide coverage for about 300,000 Arizonans who currently are uninsured. That includes childless adults whom the state stopped enrolling years ago in a budget-cutting move, and expanding eligibility beyond the current cap of the federal poverty level, about $19,530 a year for a family of three.

What that means for hospitals is fewer patients showing up without insurance and unable to pay their bills.

Gubernatorial press aide Andrew Wilder said the lawsuit amounts to little more than sour grapes.

“This is an ideological lawsuit filed by people who don’t like the AHCCCS program,’’ he said. Wilder noted voters have approved prior expansions of the program.

“We are happy to defend this in court,’’ Wilder said.

Proposition 108, approved by voters in 1992, requires a two-thirds vote of both the House and Senate for any measure that results in a “net increase in state revenues.”

But the measure does not apply to “fees and assessments that are authorized by statute, but are not prescribed by formula, amount or limit, and are set by a state officer or agency.’’

It is that exception the governor’s office is relying on to justify the legality of approving the hospital levy with a simple majority.

Sandefur argues the levy is a tax, no matter what Brewer calls it, as it is money being collected from one group of taxpayers to be redistributed for a public purpose.

Beyond that, she said the legislation gives Betlach total power, without legislative oversight — authority she contends lawmakers are powerless to give, making any funds collected or spent illegal.

Although the GOP split over the issue has prompted threats within the party about taking out lawmakers who sided with Brewer and legislative Democrats, Senate President Andy Biggs, R-Gilbert, one of the plaintiffs, said he hopes this fight does not undermine the entire session, saying the lawsuit is “not personal.’’

But it could have deeper implications.

Biggs conceded lawmakers have previously given state agencies similar power to levy “assessments,’’ which could mean the outcome limits the Legislature’s ability to allow agency-created fees in the future — and possibly undermine those already being assessed.

Biggs said he has no problem with that — that the Legislature should have been more vigilant about strictly following the two-thirds rule.