If President Barack Obama lets states restrict eligibility, it would undermine the chief goal of his healthcare law, expanding insurance coverage.
"There is a growing impatience among governors," Mike Schrimpf of the Republican Governors Association told The Washington Post. "As the Medicaid portion of state budgets grows, the issue becomes even more pressing."
This week, 29 GOP governors asked Congress for greater flexibility in Medicaid, often the biggest item in their strapped budgets.
Govs. Chris Christie of New Jersey and Jan Brewer of Arizona are seeking permission to drastically cut Medicaid eligibility for adults.
The National Association of State Budget Officers reports Medicaid took nearly 22 percent of budgets in fiscal 2010, more than schools. The share ranged from 7.3 percent in Wyoming to 37.1 percent in North Carolina.
Republicans are challenging the new healthcare law's ban on tightening eligibility.
"This law will greatly expand state Medicaid programs, pulling tax dollars from other necessary areas like education and law enforcement," Mississippi Gov. Haley Barbour has told Congress.
Like other Republicans, he wants Medicaid turned into a block grant.