How much will President Carter's new economic program really do to slow inflation?

That is the central question as the dust settles from last week's dramatic presidential announcement. The bottom line is that no one, including the administration, knows how well or badly the new package will work, and policymakers probably won't have any idea until it is way past time to change it.

In any case, no serious impact is expected for at least several months.

Carter told the nation that the budget cuts he was proposing, and the accompanying credit tightening measures by the Federal Reserve Board, were necessary first steps toward slowing the current price surge.

Urgent action was needed, he said, first to blunt the inflation psychology that was crippling the nation's financial markets, and second, to dampen the economy and cool down demand.

"I am confident that with the steps I am proposing today, the inflation rate will be declining later this year," Carter said. "As that happens, we may look forward to calmer financial markets and lower interest rates."

In fact, however, economists say the major benefits from the president's proposals won't begin to show up until well into 1981, and the package may worsen the price picture in the immediate future.

There are these considerations:

The spending reductions Carter is proposing won't take effect until October, the start of fiscal 1981, with the biggest impact not likely to come until the year is well under way.

Moreover, Carter's decision to impose a $4.62-a-barrel oil import fee will add to inflation in the short run. The move will boost gasoline prices 10 cents a gallon and raise the inflation rate by half a percentage-point.

The economy will be dampened quickly, however, by the increase in gasoline prices -- which will have the same impact as an $11 billion tax hike -- and by the Federal Reserve Board's new restrictions on credit growth.

If anything, the likelihood now is that the combination of restraints may well tip the economy into the long-elusive recession. The budget is sharply restrictive, and Americans' tax burden is rising by a whopping $52 billion.

The impact on the overall inflation rate will be slow in coming and modest at best. Although the new austerity measures may dampen demand, they won't necessarily ward off further increases in world oil prices.

Carter will get some help from a likely leveling off -- or even decline -- in mortgage interest rates, but even here the underlying inflation rate still is apt to be high, say in the range of 11 to 13 percent.

The challenge proffered by liberals is that budget-tightening alone won't do much to dampen inflation. Recent computer-model studies show that cutting spending up to $25 billion would slow inflation only 0.1 percentage-point.

But as Alice M. Rivlin, director of the Congressional Budget Office, cautioned recently, the models deal with historical behavior, and aren't equipped to take account of today's volatile conditions.

First, the computer studies ignore the impact of budget-cutting in claiming inflation psychology, which has been a major factor in the past year's price surge. They also don't count the credit-tightening and gasoline-price increase.

With new signs of some softening in the world oil markets, expected leveling-off in interest rates here and continued moderation by American labor, the new program may well end up making some progress against inflation.

Perhaps more important than how much prices will slow, however, is the question of what would have happened had Carter done nothing in the face of the past two months' turmoil.

With inflation psychology breaking out all over the nation, the bond market on the verge of collapse, businesses rushing to raise prices and borrowers scurrying to secure loans, the White House had to act or risk economic chaos.

The administration's immediate goal is not so much to slow inflation as to bring about a sharp enough recession to have an impact on prices. In that sense, the benefits in reducing inflation may not be measurable for months.