The nation's governors remain unhappy with President Reagan's proposed New Federalism program and will oppose it unless changes are made, the National Governors' Conference chairman said yesterday.

Gov. Richard A. Snelling of Vermont, a Republican, said the goal of the plan is to be "a perfect swap: no winners, no losers" in which the federal government takes over Medicaid and the states shoulder Aid to Families with Dependent Children and 35 other programs.

But four key issues remain to be resolved, he said, and they "go to the heart of the fairness of the federal initiative." A White House spokesman said the questions were still under consideration for inclusion in the legislation that will be sent to Congress by the end of the month.

Snelling said the four problem areas were the following:

* Basic short-term care for the "medically needy" in future years is not now included. The New Federalism plan would grandfather only the current medically needy, those whose medical expenses push them below their state's poverty line. The nation is expected to spend $2.1 billion for the medical needs of these people, the working poor, in 1984.

* The White House wants to keep cutting food stamp payments by 30 cents for every $1 a person's welfare benefits increase. The governors want to uncouple this link to give the states more incentive to raise benefits.

* Each state's eligibility requirements for benefits are different, and the New Federalism would leave them that way. The NGA has called for uniform national standards to go with the national program.

* The governors want the federal government to set up a special fund to help poorer states or those with sudden unemployment, like Michigan, finance adequate benefits for the poor. Washington has refused.

"We're studying the areas the governor has outlined," White House special assistant Rich Williamson said. "We realize that time is of the essence . . . . We will send a package to the Hill by the end of the month."