President-elect Ronald Reagan will have to trim nearly $15 billion from federal spending in the next fiscal year if he wants to have a chance of controlling the nation's careening economy, Senate Finance Committee Chairman Bob Dole (R-Kan.) said yesterday.

Dole, speaking on "Face the Nation" (CBS, WDVM), was the latest of a number of Republicans on Capitol Hill to paint a grim picture of the economy for the Reagan administration that takes office Jan. 20. Other Republicans have suggested budget cuts of $30 billion or more. Baker said the spending reductions would affect "everything from farm programs to Social Security -- all those things that people in politics don't like to touch."

"That's going to be very difficult to do," said Dole, adding that spending cuts should also be linked to any federal tax reduction efforts. It "means looking at a lot of entitlement programs," he said.

A similar message was delivered yesterday by James A. Baker Iii, Reagan's designated chief of staff, on "Issues and Answers" (ABC, WJLA). rWithout giving specific figures, Baker said the incoming administration will have to make "across-the-board cuts" in federal spending.

The reason is that the new administration will be working with a $60 billion federal deficit, something that was not anticipated six months ago, and that, as many economists already have suggested, will upset Reagan's plans to balance the federal budget by 1983, Baker said.

"There has been a drastic deterioration in the economy over the course of the last six months, particularly in the budget picture on the spending side . . . . No economist in the country had forecast that" development, Baker said.

However, neither Baker nor Dole yesterday would say specifically what programs are most likely to be cut. Both chose to describe cutting in terms of, as Baker put it, "controlling the growth of federal spending."

For example, cutting back on the $9.7 billion federal food stamp program that serves about 22 million people might entail "changing the eligibility requirements" governing current stamp applicants and recipients Dole said.

"We must . . . reduce the size of the pool, the number of beneficiaries, but not deprive those [really] needy beneficiaries of their benefits," he said.

Dole, also chairman of the Senate subcommittee on nutrition, said he "would guess" that he would support full refunding of the food stamp program, which expires Sept. 30.

Sen. Pete V. Domenici (R-N.M.), the new chairman of the Senate Budget Committee, already has put together a 50-page list of 193 budget cuts that he says could save between $25 billion and $29.5 billion in the current fiscal year and twice that in succeeding years. But his proposals have not been accepted, either by the GOP Senate leadership or the Reagan team.

Both Dole and Baker insisted that the new administration will have to act quickly to propose and push through Congress a spending reduction/tax cut package, although Dole expressed skepticism that Reagan can get the 30 percent tax cut he wants over the next three years.

Reagan "has maybe six to eight months to move that package through Congress," Dole said. "It's going to be hard to sustain" public support for such legislation beyond that period, he said.

Both Dole and Baker predicted that Reagan will have a tax cut/spending cut proposal ready within several weeks of his inaugural.