McConnell's remarks came as the Senate opened debate on a $5.8 billion spending plan that includes more than $1 billion in spending on caring for the state's elderly, disabled and poor.
Sen. Thomas Alexander, a Walhalla Republican overseeing the Medicaid budget, told senators the spending plan includes adding $435 million just to keep existing Medicaid programs operating.
McConnell, a Charleston Republican, said that's too much of a drain.
"How is this state going to sustain this?" McConnell asked. "I'm told we don't have school buses funded in this bill. Not a nickel to replace a school bus and yet we could come up with $200 million-plus to bail this program out of a deficit? I don't understand the priorities in this state."
Alexander said the state hasn't changed its Medicaid program to make the benefits more generous or expand who is eligible. He said the priorities are right because the program takes care of needs of the disabled, people in nursing homes and the growing ranks of children who had access to health insurance until their parents lost jobs in the recession.
But McConnell didn't back away from the criticism.
"I see it as a program that, year after year, we dump millions and millions more in," McConnell said. "It's growing faster than the rest of state government and it's just eating up every available dollar for higher education, K-12, school buses and everything. We can't stay on this course.
The spending plan's debate isn't what many had expected earlier this year.
Legislators began writing the budget fretting over a more than $700 million gap between revenues and expected spending.
Budget writers were warned the Medicaid program had a $635 million shortfall for the fiscal year that begins July 1.
Legislators are covering $157 million of that with a cigarette tax increase approved last year. Health and Human Services came up with $200 million in spending cuts, including saving $125 million by reducing payments to Medicaid providers.