AUGUSTA — Maine’s health and human services commissioner said Friday her department only has enough money to pay its bills through June 10. That’s 20 days before her department’s accounts would be replenished by a new state budget.

Commissioner Mary Mayhew included the news in a letter sent Friday to Gov. Paul LePage, in which she said lawmakers need to pass a budget by May 28 so her department can make its payments.

“Without a new budget to address the immediate need for funding through the remainder of this fiscal year, we will not have enough money to pay all of our providers,” Mayhew wrote in the letter.

Mayhew’s letter prompted a more terse letter from Gov. Paul LePage to legislative leaders, in which he called on Democrats to propose an alternative to his unpopular budget proposal.

“If a budget is not approved, the Department of Health and Human Services will run out of money in three weeks,” LePage wrote. “Starting the week of June 10, DHHS will not be able to pay for services for our most vulnerable Mainers. Democratic leaders are so focused on expanding welfare to cover able-bodied people, they have forgotten about the Mainers who are already on Medicaid.”

In committee, Democrats have voted to tie repaying the state’s $484 million debt to its hospitals to an expansion of Medicaid, something LePage and many other Republicans oppose.

“While Democratic leadership is engaging in Washington-style politics and strong arming members of its caucus to vote against the wishes of the Maine people, a crisis is looming that will affect our most needy citizens,” LePage wrote.

Democratic leaders questioned why LePage sent a letter to them on a Friday evening rather than request a meeting to discuss the urgent news. Alfond and Eves also requested Mayhew appear before the Legislature’s budget-writing Appropriations Committee on Sunday to answer questions. The committee is holding weekend sessions as the Legislature’s June 19 adjournment date approaches.

“The timing and intent of this letter is questionable,” Eves said in a prepared response. “It seems more geared toward fear mongering than problem solving. We have been pleased with the bipartisan work of the Appropriations Committee for the last five months. In order for their work to continue, we must get answers.”

Alfond said Mayhew needs to “address the administration’s potential mismanagement of this situation.”

Members of the Appropriations Committee are at work crafting a budget compromise based on LePage’s original proposal, though they haven’t reached a final accord. They have yet to address recommendations from other legislative committees that oppose a number of LePage’s proposed cuts and propose $30 million in additional school funding.

LePage spokeswoman Adrienne Bennett called the letters from LePage and Mayhew “a friendly reminder of where we’re at and that action does need to be taken.”

The LePage administration last week rolled out a package of changes to the governor’s biennial budget proposal that includes $35 million so the state Department of Health and Human Services can meet its immediate needs.

Bennett said the LePage administration is holding out hope that lawmakers will pass the $35 million budget addition as part of LePage’s full two-year budget proposal. If that proves impossible, the administration could propose an emergency budget package.

“We do have means to address this issue if need be,” Bennett said, “and the governor, of course, will see that the state of Maine pays its bills.”

LePage, in his letter, repeated his accusations that Democrats have been stoking fears of a government shutdown, which would occur if a budget is not passed by July 1.

“A shutdown is determined by law, not by a governor,” he wrote. “If the Legislature fails to pass a budget, I have no authority to spend money. With no money, government shuts down. But I am not planning for a shutdown. I submitted my plan five months ago. What is your plan? Mainers deserve to know.”