The White House yesterday moved to quash expectations that passage of the tax-cut bill will revitalize the economy immediately, expectations it may have generated in its campaign for the cuts.

Americans should not "expect too much too soon," presidential spokesman David Gergen said yesterday.

But he denied that the administration was backing away from claims about the effect of the tax cuts. On Wednesday President Reagan said he expected the "fact of the passage" of the bill to have an immediated psychological impact.

Gergen said he was not trying to qualify Reagan's comments. He stressed that the tax cuts "will be a genuine tonic for growth," but will not make the economy "turn on a dime."

Murray Weidenbaum, chairman of the Council of Economic Advisers, briefed Reagan yesterday morning at a meeting of top administration economists. Weidenbaum told Reagan that the economy is still weak and that the tax-cut bill would help more in the long term than in the immediate future, Gergen said.

But "we expect to see and upturn by the end of the year," he added.

He also said, "We do continue to foresee an abatement on interest rates," which so far have remained stubbornly high. Administration and White House officials have been hoping that rates will begin to drop from their current record levels once the president's economic program is in place.

However, officials recently have refused to say precisely when they expect interest rates to fall. A Treasury spokesman yesterday said that rates should be lower by winter.Reagan's latest economic forecast assumed an early sharp fall in rates.

The administration is pleased by the decline in inflation so far this year, Gergen said, adding that as inflation drops so will interest rates.

Reagan emphasized at the meeting with advisers that continued budget cuts will be necessary to revitalize the economy, Gergen said. Budget director David A. Stockman is looking for a further $30 billion of as-yet-unspecified cuts for 1983, rising to $44 billion by 1984, to meet the balanced-budget target for that year.

These numbers do not include the projected savings from the administration's controversial Social Security proposals, nor about $10 billion Congress still has to cut from the 1982 budget.

Weidenbaum believes "we do have a soft, soggy economy" but that "1982 will be a year of encouraging growth," Gergen said.

Weidenbaum likened the economy to a feverish patient, Gergen said: "If a person has a temperature of 104 degrees, there is no medicine that will bring instantaneous relief, but you can begin applying remedies that will restore full health, and that's what this program is designed to do.c

Many economists doubt whether Reagan's promise of accelerating growth, combined with lower inflation and interest rates, can be achieved.

One reason the tax-cut bill will not immediately turn the economy around is that the 25 percent cut in individual tax rates will be phased in over 33 months, Gergen said.