The nation's governors came away from a meeting with President Reagan yesterday without assurances that the president intends to do anything to help ease cutbacks in domestic spending required in the budget balancing act.

"I just didn't get the sense that the president is going to do anything more than about what he has done," said Kansas Gov. John Carlin, a Democrat. "He is going to sit and wait."

Governors, gathered for their annual winter meeting, said Reagan gave them a sympathetic ear, but little else in their 40-minute discussion, which was described as less contentious than others in recent years. "It was the most open dialogue we've had," said Arkansas Gov. Bill Clinton, a Democrat and vice chairman of the National Governors' Association.

"We weren't there to make a deal with him," said Tennessee Gov. Lamar Alexander, a Republican and chairman of the association.

"In some ways, he [Reagan] has almost worn us down," added Carlin, chairman of the governors' budget committee. He said the delegation of 45 governors told the president that they were resigned to accepting significant cutbacks, but wanted them to be done "reasonably."

Governors said their sharpest complaints centered on the administration's handling of the beleaguered farm economy and its attempt to shift Medicaid program costs to the states.

"I don't think his advisers are even keeping him informed on the extent of the farm crisis," Iowa Gov. Terry E. Branstad, a Republican, said, adding that Reagan seemed surprised to learn that he has failed to make appointments to empty seats on a new board to oversee the Farm Credit Administration. "We've got a crisis in agriculture and no one is in charge."

The governors proposed to Reagan that Washington take over all Medicaid costs and that states take over all highway programs except the interstate highway system. In return, the states would get the revenue from the 9-cents-a-gallon federal gasoline tax.

Reagan's 1987 budget proposal would cut the federal contribution to Medicaid by $1 billion and limit the current system of open-ended federal grants to states, cutting another $1.1 billion. The Medicaid reduction is to be partially offset by a $300 million one-time grant to help states with unusually high Medicaid expenditures.

Democratic governors yesterday were drafting a statement that condemned the new Gramm-Rudman-Hollings budget-balancing law as an "abdication" of federal responsibility. Several Democrats complained that the president was attempting to shift responsibility for government programs to the states without giving them the money to pay for them.

Michigan Gov. James J. Blanchard, a Democrat, said the White House session appeared designed to mollify the governors. "Every other sentence was a compliment on what a fine job the states are doing," he said. "They clearly believe that federalism means shifting the burden back to the states. Clearly, they're not against raising taxes, they just want the states to do it."

"It was vintage Reagan," said Arizona Gov. Bruce Babbitt, a Democrat. "He was tremendously relaxed. He appeared to having nothing else to do and it was utterly devoid of substantative content."

The governors had better luck with another concern -- the deductibility of state and local taxes in the pending tax bill. New York Gov. Mario M. Cuomo (D) said Rep. Dan Rostenkowski (D-Ill.), chairman of the House Ways and Means Committee, and Rep. James C. Wright Jr. (D-Tex.), the House majority leader, "told me they won't let out of conference any tax bill with any compromise on deductibility."