Federal Reserve officials are worried that White House insistence on sticking with an overly optimistic economic forecast will spell trouble in 1982.

The Fed's own staff expects the economy to be much weaker next year than forecast by administration economists, who are still predicting a 5.2 percent rise in the gross national product, after adjustment for inflation, during 1982. In contrast, the Fed forecast calls for little if any growth in output between now and the middle of the year, and even a moderate recovery after that will be dependent on continued improvement in inflation.

Officials at the Federal Reserve believe the administration's determined optimism has already added to its credibility problems in financial markets. And continued disappointment over the nation's economic performance during the next several quarters, they fear, could undermine political support for the Fed's basic policy of slowing growth of the money supply to curb inflation, which has the administration's fervent backing.

Some private economists who support President Reagan's general approach are also concerned over administration claims about a quick economic recovery and sharply lower budget deficits. Rudy Penner, former chief economist for the Office of Management and Budget in the Ford administration and now at the American Enterprise Institute, declares, "The most important thing now is credibility. It would almost be better if they were too pessimistic."

More realistic numbers are circulating within the administration, too, but so far they are being kept under wraps. When Reagan made major revisions in his 1982 budget proposals last week, no changes were made in any of the economic assumptions except for the level of interest rates, which was hiked by more than 2 percentage points from estimates made in July.

Murray L. Weidenbaum, chairman of the Council of Economic Advisers, last week told the House Budget Committee, "Since mid-June several events have taken place which might suggest modifications in the forecast for 1982. . . however . . . no event of sufficient magnitude has taken place which would call for a full-scale revision . . . ."

The Reagan economic team this week will begin cranking up its computers to produce just such a full-scale revision, on which planning for the 1983 budget will be based. The revised forecast will be published in January as usual, along with the new budget.

Some of the less optimistic administration economists are bracing themselves for a debate every bit as contentious as the one last winter that preceeded the first Reagan forecast. At that time, some of the economists were counting on a spontaneous drop in inflation expectations to produce both lower inflation rates and lower interest rates in the face of a very tight monetary policy.

The nation's underlying inflation rate has come down somewhat, though the consumer price index was up 10.9 percent in the 12 months ended in August and rose at an 11.5 percent annual rate in the latest three months. Much of the improvement this year was due to steady food prices and falling oil prices rather than a sea change in inflation expectations. One consequence is that long-term interest rates, which reflect such expectations, remain at historically high levels.

Economists at the Treasury Department, devoted adherents to so-called supply-side economics, are expected to stick with predictions of strong growth that will occur as a result of the large cut in personal and corporate income taxes. Others at the CEA and the Office of Management and Budget will take a more traditional approach, albeit from a monetarist point of view in the case of Jerry Jordan at the CEA.

Federal Reserve officials believe the Reagan economic forecast is too rosy primarily because of some inescapable monetary arithmetic that the administration implicitly denies.

Usually, any increase in total national income tracks the increase in the money supply, plus an increment known as velocity -- the rate at which a given dollar is turned over. These relationships are far from fixed, but over a period of time they apparently do hold.

The most closely watched measure of money, M1-B, which includes currency in circulation and checking deposits at financial institutions, is intended by the Fed to grow next year by between 2 1/2 percent and 5 1/2 percent. If the velocity of M1-B rises at its long-term trend rate of about 3 percent, then national incomes should rise 5 1/2 percent to 8 1/2 percent.

But even optimists on inflation -- including the administration -- expect inflation in 1982 on the order of 7 percent. Such an increase in prices would absorb all or nearly all of a rise in incomes that fell within that 5 1/2 percent to 8 1/2 percent range. It would leave no room at all for a big jump in real income such as the 5 percent-plus forecast by Reagan.

Federal reserve officials say they are committed to slowing the growth of money over several years to combat inflation, and as of now, they are aiming at the mid-point of their range for M1-B, which is 4 percent growth. Moreover, if the level of M1-B or any of the other monetary aggregates for the fourth quarter of this year comes in below Fed target levels for this year, there is no intention of "ratcheting up" the starting point for calculating next year's goals.

If the Fed hews to such a policy line, there simply will be little money available in 1982 to support real economic expansion -- unless inflation drops below expected levels. This is the reality of the Fed targets, which officials at the central bank say top administration economists will not acknowledge.

Several other forecasters are equally loath to accept the monetary arithmetic.

The Congressional Budget Office, for instance, in its latest forecast calls for a 4 percent rise in real output during 1982, assuming M1-B growth would be at the top of the Fed's range and that velocity would rise 5 percent.

And a telling passage of the latest forecast by Data Resources Inc., the economic consulting firm, declared, "The 10 percent tax reduction of mid-1982, along with the cost-of-living adjustment of Social Security benefits, will create a budget stimulus to purchasing power of $43 billion. With the crucial congressional elections just four months away, the Federal Reserve will then face a grim dilemma whether to accommodate this stimulus.

"The DRI forecast assumes that the Fed reaction will be very mild, with both long- and short-term interest rates rising little more than 1 percentage point , and the money supply allowed to rise at the upper end of the target range during those months. This is one of the high-risk assumptions in the forecast: the Federal Reserve could let the recovery proceed at a faster pace, or it could choose to convert the entire fiscal stimulus into higher interest rates, monetary restraint, and crowding out of private expenditures by the enlarged federal deficits," DRI said.

The CBO forecast, to say nothing of the administration version, also assumes that the unusually large increase in velocity that is assumed to occur will take place in the context of falling interest rates. Historically, however, rising interest rates have been the force driving people to reduce their cash and transaction account balances, because it meant it was costing them more -- either in interest paid if they had borrowed money or in interest foregone if they failed to invest their funds.

Federal Reserve officials even go a step further. What if the public does become convinced that inflation is coming down? The present trend in velocity was established over a long period of time in which expectations of inflation were rising. Might it be, they ask, that a shift in expectations could cause a shift in that trend line, meaning that a given rate of expansion of the money supply would support an even smaller rise in economic activity?

The officials do stress that these calculations might not, in the end, apply to 1982. A few years ago, for example, an unexpectedly large rise in velocity fulfilled a real growth forecast made by the Fed chairman at the time, Arthur Burns, that had been questioned by many economists.

Nevertheless, the validity of the picture in the administration's crystal ball, as well as in that of several private forecasters, seems to hinge on assumptions that either there will be a historically large jump in velocity or that the Fed will not pursue successfully the policy of monetary control that it has announced.

Certainly, given the tough talk of Federal Reserve Chairman Paul Volcker in his recent appearances, including a speech to the National Press Club last week, the battle against inflation "is far from won."

"Indeed, I believe we are just entering the crucial stages," Volcker said. "One crucial element in 'carrying through' is persistence in monetary policy -- continuing to bring down excessive growth in money and credit . . .

"I . . . believe there is now ample evidence that we mean what we say, that the trend of monetary and credit growth is slowing, and that our purposes are clear in our actions," he said.