Brad Johnson, New York State government's representative in Washington, was incorrectly identified as Brad First in an article in The Post yesterday.

The federal trust fund proposed by President Reagan to finance more than 40 programs that would be turned back to the states as part of his New Federalism is several billion dollars short of what it would cost to sustain those programs at current levels, administration officials acknowledged yesterday.

Administration officials, in describing the president's proposal earlier this week, said it would not cost the states any money when it started in fiscal 1984.

The trust fund would be financed out of federal excise taxes and the federal windfall profits tax on oil. These would be adequate to pay for the 40-plus programs until they were turned over to the states later in the decade, officials said.

But what they failed to mention was that before shifting these programs to the trust fund they planned to cut them substantially in the fiscal 1983 budget, which the president will send to Congress next month.

"I was ready to tell anyone who asked," Edwin L. Dale Jr., spokesman for the Office of Management and Budget, said of the plan to cut the programs before shipping them off, but "why emphasize it?"

He said the new cuts, and the difference between earmarked funds and current costs, would be "less than $5 billion."

"We made it clear to governors that we are proposing further cuts," said Richard S. Williamson, the president's assistant for intergovernmental relations. "It isn't anything we're trying to hide."

Williamson and Dale also said yesterday that if Congress does not approve the new cuts the administration will adjust its plan to make sure that the states do not lose in the plan's first year. This is a "starting principle" of the federalism plan, Dale said.

Either the trust fund would be increased or the number of programs to be returned to the states reduced to keep the states whole, he said.

Williamson, one of the key aides involved in drafting the federalism plan, sought to separate it from the coming battles to cut domestic spending. He said the questions being raised about spending levels came from people who wanted to "continue on the liberal agenda that was rejected by the voters."

"The real question is what is the goal and the goal is we want to try to return equivalent revenue sources with the responsibility."

The discovery of the funding discrepancy came when Brad First, Washington representative for the state of New York, and analysts for the American Federation of State, County and Municipal Employes (AFSCME) added up the current costs of the 43 programs that the administration has suggested could be returned to the states.

They found that it was considerably larger than the $30.2 billion the administration had included in its calculations.

"What you've got here is a shell game with no pea," said Joe Beeman, director of political and legislative affairs for AFSCME.

"I think it's disingenuous of them to say there are no winners and losers," said First. "All states are losers."

The 43-program trust fund is one part of the Reagan plan. The fund would be kept at its starting level for four years, then reduced as the supporting taxes were phased out. Ultimately the 43 federal programs would cease to exist; states could continue them and raise the revenue to pay for them or not, as they chose.

In addition, Reagan proposed a swap in 1984 under which the federal government would take over the state share of Medicaid while the states assumed the federal share of Aid to Families with Dependent Children plus the food stamp program, now all federal. Administration officials said this, too, would come out even.

But officials conceded that to make it do so they assumed Congress would also make some cuts in AFDC and food stamps this year that would reduce by $3.7 billion this burden the states would be taking on.

Questions yesterday about the trust fund came amid a rising clamor from liberals, Democrats and big city mayors about both the president's federalism initiative and the coming proposals for cuts in the federal budget.

"Mayors know that the most basic needs of city residents will not be met in the months ahead unless the cuts in federal urban programs are stopped, and stopped now," said Mayor Helen Boosalis of Lincoln, Neb., the president of the U.S. Conference of Mayors.

Americans for Democratic Action President Robert F. Drinan criticized plans to shift welfare and nutrition programs to the states, saying "the real revolution in Reagan's address is his plan to allow the states to phase out these programs."

National Urban League President John Jacob, who met with the president yesterday, said he had told Reagan, "It was not in the best interest of AFDC recipients to have a program so vital to the survival needs of poor people transferred to states who traditionally have demonstrated that they do not manage social programs very well."