Washington — The marble halls of the Federal Reserve Building here are spacious and cool, but the atmosphere must be heating up as pressure mounts on the nation's central bank to do something to bring down interest rates.
''In the very short term,'' says Murray Weidenbaum, chief economic adviser to President Reagan, ''the trend is toward higher interest rates.''
''Painfully large'' budget deficits, Mr. Weidenbaum told reporters at breakfast, plus a money supply growing faster than the Fed's 1982 targets, prod interest rates up.
Until those rates come down, analysts agree, the economic turnaround that may now be beginning has little chance of taking root and becoming a full-fledged recovery.
Latest evidence that the recession may be over came in a government report that the index of leading economic indicators - a collection of measurements designed to show the future course of the economy - has risen three months in a row.
Prior to March 1982 the index had fallen consistently for a year. Three months of growth - 0.2 percent in March, 1.3 percent in April, and 0.3 percent in May - indicate that the corner may have been turned.
''Growth in consumer income,'' says Mr. Weidenbaum, ''translates into growth in consumer spending. The consequence (will be) an expansion led by consumers.''
Lower inflation, the July 1 tax cut, and a 7.4 percent boost in social security benefits are among reasons White House officials expect a consumer-led rally to start.
Traditionally business investment provides the second stage of recovery. How robust that will be this time depends on what Mr. Weidenbaum calls a ''serious problem'' - the performance of interest rates.
There's pressure on the Fed from Congress, especially in the House, to ease credit, making it easier for businessmen and individuals to borrow money.
This approach is rejected by Fed chairman Paul A. Volcker and most of his fellow governors, on the grounds that gains made against inflation might be lost.
Much of the credit for reducing inflation is given to the Fed's tight-money policy, though at the cost of deep recession and the highest unemployment rate since 1941.
Beryl Sprinkel is one of Treasury Secretary Donald T. Regan's top aides and, as undersecretary for monetary affairs, the highest-ranking monetarist in the Reagan Administration - a man who believes that inflation springs primarily from too-rapid growth of the money supply.
Messrs. Regan and Sprinkel applaud the Fed's tight monetary goals, but criticize Volcker and crew for what the Treasury calls erratic swings in the money supply.
The Fed has the right idea, but implements it poorly, in the Regan-Sprinkel view. Both men want the Federal Reserve Board to smooth out money-supply behavior and reduce uncertainty in financial markets.
Some critics interpret this partly as an effort to get an administration handle on the Fed, perhaps through a board seat for the secretary of the Treasury.
Mr. Weidenbaum said that his agency, the Council of Economic Advisers, was not involved in a substantive review of the Federal Reserve System beyond the ''constant review and monitoring of the course of monetary policy.'' Saying ''I am not a Fed basher,'' he avoided direct criticism of central-bank performance.
The Fed's operational independence of Congress and White House, says Mr. Volcker, minimizes political influence in the management of the nation's money.
So far this year the Fed has been above its growth targets for various categories of the money supply, especially M-1, the most widely watched of all.
M-1 includes currency in circulation, plus regular and interest-bearing checking accounts. These are called ''transaction'' accounts to distinguish them from savings accounts, which belong to M-2, another category.
Since the fourth quarter of 1981, according to the Argus Research Corporation , M-1 has grown at a 6.7 percent annual rate - well above the upper end of the 2 .5 to 5.5 percent range targeted by the Federal Reserve Board. M-1 rose especially fast during the first quarter of 1982.
This high rate of growth in the money supply, according to Treasury officials , makes lenders uneasy, because it indicates either that inflation may rise or that the Fed may tighten the screws on M-1. Anticipating these results, lenders keep interest rates high.
Fed officials reply that the excess of M-1 over the upper range of the target is primarily technical and should not be destabilizing to the markets.
Since the introduction of interest-bearing, or NOW, checking accounts, many people have shifted funds from passbook accounts (M-2) to NOW instruments (M-1).
Since last fall, says Fed governor J. Charles Partee, ''there has been a good deal of precautionary buildup in NOW accounts. This accounts for a disproportionate amount of the increase in M-1.''