The first Commerce Department projections for second quarter gross national product, released last week, immediately renewed a dispute within the Reagan administration over how fast the economy is apt to grow in the second half of 1983.

At the Treasury Department, the economists remained as bullish as ever on the outlook. Undersecretary for Monetary Affairs Beryl Sprinkel took the latest Commerce estimates--which show GNP, adjusted for inflation, rising at a 6.6 percent annual rate this quarter--as confirmation that real growth this year will turn out to be closer to 6 percent than the 4.7 percent the administration officially predicted in April.

On the other side of the White House in the Old Executive Office Building, Martin S. Feldstein, chairman of the Council of Economic Advisers, told reporters that the recovery was not as strong as the numbers seemed to imply. While the 4.7 percent figure might well be revised upward when the administration reassesses its forecast next month, any change likely will not be large, he indicated.

GNP growth for the quarter is turning out higher than many forecasters were predicting early this year, though some economists, including those at Wharton Econometrics, were not far from the mark. Much of the increase in production, however, is flowing into business inventories rather than into final users' hands, one of the reasons for Feldstein's caution.

The administration's disagreement over the short-term economic outlook, which is mirrored to a lesser extent in the predictions of private forecasters as well, involves more than just a quibble over details of a forecast.

For Sprinkel to be right, the economy would have to continue to grow at a pace comparable with that for the second quarter. Administration officials in the past have argued that such a fast recovery could reignite inflation despite the high level of unemployment and of unused production capacity.

Such a rapid recovery probably would cause the Federal Reserve to clamp down on money supply growth and let interest rates rise. The Commerce estimates show GNP in current dollars rising at more than a 10 1/2 percent annual rate this quarter, while the Fed has set its money supply targets to achieve something closer to 9 or 9 1/2 percent.

Some Federal Reserve policy-makers are already upset at the unexpectedly swift increase in M1, the money supply measure that includes currency in circulation, checking deposits at financial institutions and travelers checks. M1 is up at more than a 15 percent annual rate so far this year from its fourth quarter level. The Fed's target range, on the other hand, is 4 percent to 8 percent for the four quarters of 1983.

Interest rates have also been rising recently as more financial market participants have come to expect an imminent Fed tightening. In general, forecasters are revising their interest rate predictions upward along with their estimates of real GNP. Instead of additional small declines, the typical forecast now shows flat or moderately rising rates.

Rates paid by banks on large negotiable certificates of deposit have climbed almost a full percentage point in the last six weeks to about 9.2 percent. That rise means that the spread between the CD rate and the banks' 10 1/2 percent prime lending rate is only 1.3 percentage points, only half the average spread for the last 12 months. If short-term rates don't bob down again, the prime undoubtedly will go up soon, according to a number of analysts.

Long-term rates have also gone up, though by less than short rates.

The members of the Fed's policy-making group, the Federal Open Market Committee, were sharply divided at the FOMC's last meeting over whether to take steps immediately to slow the growth of M1. The Fed will not release the minutes of that meeting until after the next FOMC session, scheduled for July 12-13, but one Fed official described it as "a corker."

The strong second quarter expansion strengthens the position of those FOMC members who argue that the high M1 growth is partly a consequence of rapidly rising real economic activity, not just some sort of aberration. If M1 growth does not slow of its own accord between now and the July FOMC meeting--often volatile on a weekly basis, M1 fell by $3.2 billion in the week ended June 15--the odds greatly favor some mild steps to tighten policy, which likely would mean somewhat higher short-term interest rates.

To the extent that the bullish outlook of the Treasury is accepted by the FOMC members, the more restrictive those tightening actions would be. Treasury officials and Feldstein, as well as a number of private economists, have said money growth must be reduced even if interest rates rise as a consequence.

At the same time, Fed officials are deeply concerned about the dangers posed for the international financial system by the possibility that a number of developing nations will default on their international loans. Rising interest rates would heighten that possibility, and for that reason, the officials will be very reluctant to see rates rise very far.

The fundamental reasons for rising interest rates, Feldstein said, are "a large federal budget deficit and the recovery, not a change in inflationary expectations. With the recovery picking up, private credit demand is increasing. What will happen to the market clearing real interest rate? It will be rising."

Feldstein said the broader monetary aggregates "haven't done anything at all disturbing . . . and the M1 recently is a real puzzle. I don't know frankly how much weight to put on M1 at the moment . . . But you can't give it zero weight. It would be good to see M1 moving back very gradually to the upper end of the target range that the Fed set."

Then the CEA chairman candidly acknowledged, "I think interest rates may well have to go up as part of that process." Just how much is hard to say since part of the recent increase in rates likely was the result of the market's anticipation of a Fed tightening. If the tightening does occur, validating the market expectation, rates would not necessarily go up all that much more.

Feldstein does not think even a further increase in rates would stop the recovery in its tracks. One of his predecessors as CEA chairman, Alan Greenspan, made the same point last week in testimony before the Joint Economic Committee.

"There is an awful lot of momentum in any recovery," Feldstein said, "and this one is being fed by tax cuts . . . the principal effect of high interest rates is to change the character of recovery rather than end it. We do run the risk that this lopsided recovery will not sustain itself."

Greenspan stressed timing in his testimony. "The high level of real short-term interest rates is not a significant inhibitor of economic recovery at this stage of the business cycle," he told the JEC. "Even a modest rise in rates from current levels is unlikely to abort the currently unfolding expansion . . . When short-lived items such as nondurable goods and services are involved, financing is not a critical factor in determining production levels."

But later in the recovery, business investment in plants and equipment and in inventories will require financing. Similarly, the strong housing recovery could well run into financing difficulties if mortgage rates were to continue for long their recent increases.

More immediately, the high level of rates relative to inflation is keeping the value of the dollar high on foreign exchange markets and adding to the United States huge merchandise trade deficit, which Feldstein expects to reach a record $60 billion this year. As strong as the second quarter has been, a sharp drop in net exports nevertheless lopped more than $20 billion off current dollar GNP.

The CEA chairman pointed to the trade sector as a "unique" feature of this recovery. "It's one of the purest examples of how expectations of large budget deficits in the future have an impact on the recovery. The deficits lead to high real rates and a high value for the dollar which produces this trade imbalance," he said.

In support of the notion that the recovery is not quite as strong as it looks, Feldstein said that final sales--that is, GNP less the change in business inventories--are rising at only a 2.5 percent annual rate this quarter following a 1.3 percent increase in the first quarter. That 1.9 percent average for the first two quarters of the recovery compares with an average of 5.1 percent for the first half year of the seven other post-war recoveries.

The 10 percent cut in withholding for personal income taxes, due later this week, will add to disposable personal income at about a $30 billion annual rate, an amount equal to nearly 1 percent of GNP. That should help bolster consumer spending, though a sizeable chunk of the additional take-home pay likely will be saved, at least in the short run.

Personal saving as a percentage of disposable personal income fell to 5.3 percent in May, well below last year's 6.5 percent rate.

Remarkably, personal consumption spending, after adjustment for inflation, has gone up in each of the last six quarters. (See chart.) As bad as the recession was, it would have been worse had consumers not consistently spent more than expected.

The amount of money going into housing construction, one of the brightest sectors of the economy, is not expanding as rapidly as the level of new starts would indicate, Feldstein also said, because many of the units being built are smaller than in the last recovery.

With business fixed investment and government spending for goods and services rising relatively slowly, except for defense purchases, two other sectors are not expected to add significant strength to the recovery in the second half of the year. Meanwhile, because of government programs to reduce farm surpluses, farm output is falling.

Finally, the major source of additional demand in the second quarter--the change in business inventories--should be a smaller but still positive factor.

It is a standard warning of economic forecasters that recoveries often surprise everyone with their strength. That could happen again this year, but the second quarter figures don't guarantee that it will. After all, interest rates have never been this high relative to inflation during the first year of a recovery. Nor has the Fed been as willing to let rates rise to keep inflation in check in the future. By historical standards, it remains a whole new ball game.