Washington — The failure of President Reagan and Congress to reduce the federal deficit is forcing upon the Federal Reserve Board a responsibility for which it was not designed, nor instructed by voters to execute.
The Fed must make what one banker called ''social and political policy'' by deciding, in effect, how fast the economy should grow, how many people should be unemployed, and what the inflation rate should be. In the process, the central bank's decision also affects United States foreign trade and relations with other countries.
This is why frustration with the White House and Capitol Hill lies close to the surface these hot days of August, as Federal Reserve officials discuss what one calls a ''terrible dilemma.''
''The domestic economy may require higher interest rates to hold down inflation. But higher US rates are exactly the wrong thing for the rest of the world,'' he says.
Fed officials have lost hope that the Reagan administration and Congress will lend an early hand in resolving the problem.
''I think that (the Reagan administration) has made peace with large deficits ,'' says another banking expert. ''I find this surprising for conservative Republicans, who have always blamed Democrats for running deficits.
''At some point, the Fed tightens credit further, or the economy will do it by itself,'' the banker adds.
''The monetary aggregates (money supply) will grow,'' he replies, ''and the financial markets will decide that the Fed is not going to move. So the markets will raise interest rates protectively.''
Two signals came from the markets Monday. Major banks raised their prime rate - the key interest rate they charge their best corporate customers - from 10.5 to 11 percent. This brings the prime more in line with the general rise in short-term rates that has occurred since late May.
Wall Street, interpreting the move to mean that higher interest rates are on the way, sent the Dow Jones industrial average plunging 20.23 points to 1,163.06 , the lowest closing since April 13.
''I think the domestic economy can stand a bit of credit tightening without jeopardizing the recovery,'' said the central banker. ''But I'm not sure about the effects overseas.''
He ticked off the ''cons'' to boosting interest rates in the US: ''The dollar grows stronger, throwing it more out of line with other currencies. Other (countries') central banks are forced to raise their rates, slowing down world recovery. Debtor countries find it harder to pay what they owe. World trade declines.
''If a nation like Brazil (which owes $80 billion, much of it to US banks) were simply to wash its hands of its debt,'' says the banking expert, ''US bank regulators would be required to reclassify loans made by lender banks.''
Some experts say this might put a few banks out of business and cause a run on others, as worried depositors withdrew their money. Other analysts deny that this would happen, even if more than one debtor nation defaulted.
''Certainly we at the Fed are aware of the debt crisis,'' says the Federal Reserve official. ''But we are also concerned that the US, if the recovery comes too fast, could lose some of the gains against inflation.''
Such is the dilemma with which the Federal Reserve grapples, as competition for capital between huge Treasury borrowings and a resurgent private sector grows.
Some analysts say they expect the prime rate to move higher, since Monday's rise does not fully compensate banks for the increased interest rates banks have had to pay to attract deposits.
The ''spread'' between what banks earn on loans and what they pay out in interest is considerably smaller than it was a few months ago, even with the prime-rate hike to 11 percent.