Ten weeks after embarking on a new economic program to manage the heavy national debt, Argentina has put in question its ability to implement the plan because of the ruling military's fragmented authority and building political pressures as the country moves toward elections late this year.

The program was painstakingly worked out with foreign private bankers and the International Monetary Fund. But in an indication of the current state of leadership here, the government has not been able to agree publicly even on just how big the foreign debt is.

Late last year, Jorge Wehbe, the third economy minister to grapple with Argentina's finances in the last nine months, announced that the debt was $43 billion, exceeded in Latin America only by Brazil and Mexico and one of the highest in the developing world.

Then last month, the Air Force, representing one-third of the military government, launched its own investigation of the country's finances and concluded that the debt was $37.8 billion. Wehbe suddenly answered that it was $37 billion; then the Central Bank reported that it was $38.7 billion.

Outraged politicians demanded to know who was right. There was sudden pressure for Wehbe's resignation, and dark suggestions about missing billions. Government authorities, meanwhile, only increased the debate when they answered that they had made a miscalculation that amounted, the Central Bank president said, to "a millimeter's difference."

For bankers and financial analysts here, the controversy illustrated how Argentina's financial health--and its ability to meet foreign debt payments--hinges on governmental coordination and public confidence that the divided authorities are hard pressed to control.

Government officials, bankers and diplomatic experts tend to agree that the $2.1 billion IMF loan package and commitments by private banks to reschedule more than $12 billion in debt payments--and lend $1.5 billion more--put Argentina in position to meet its external obligations this year without further emergency measures.

But while debate over the very size of the foreign debt flourishes, "there could be pressure from below both in and outside the armed forces to take actions that undermine the program," one diplomat said. "The negotiations are going to be very tortuous, but the big banks have confidence that they are going to get paid," he added. "The main doubt is the political situation."

While economic authorities appointed by President Reynaldo Bignone have worked to implement the economic program and refinance the debt, parallel economy offices in the armed services have reached their own conclusions--and the Air Force has even released its findings.

Through the ruling military junta, Air Force leaders and other military chiefs have in the past pressured or blocked Argentine economy ministers, and persistent reports in recent weeks have said that the junta has issued at least general instructions to Wehbe.

Meanwhile, some political leaders scrambling for position have seized on the foreign debt as an issue of nationalism. One leader of the Radical Party, Luis Leon, said in a recent press conference that "the government has got to decide whether it is going to listen to the International Monetary Fund or the Argentine people."

The position of the left wing of the leading Peronist party, meanwhile, was captured recently by a cartoon in the faction's newspaper, La Voz. It showed Wehbe bending over to pick up a single shiny coin off the ground as Uncle Sam's boot headed for his rear. "Wehbe promised that the debt would be paid, though it be through the hunger and thirst of the population," read the caption.

So far, Argentina's major labor organizations and presidential candidates have yet to launch such strong attacks, in part because the economy has undergone a mild recovery after a 12 percent drop in the gross national product in the last two years. Wages rose by 5 percent in real terms in the last months of last year, and a record grain harvest for the large agricultural sector has all but assured Argentina a comfortable surplus in its trade balance.

The Argentine financial program agreed with the IMF "is an expansionary one," said a high Central Bank official, who spoke on the condition that he not be named. "We are not like Brazil and Mexico, that have to force a recession to achieve the necessary balance of payments. So there are not great sacrifices to be made."

Many economic analysts and business leaders agree that the government program does not necessarily impede economic growth. It includes increases in public utility prices, regular currency devaluations and a reduction in the government's fiscal deficit but also calls for increases in public investment.

But both businessmen and officials say they are concerned that the government's diminished political authority could negate efforts to meet the agreed-upon guidelines.

This could block later installments of the IMF aid, or result in further economic deterioration and greatly increase political opposition to its enforcement.

The most serious problem--and the major departure so far from the goals of the IMF agreement--is inflation. Argentine officials set a goal with the IMF of a 160 percent inflation rate for l983, a 50 percent reduction from l982. Even so, the Central Bank official observed, that level "is something the IMF would not normally agree to."

But prices already have risen 31 percent in the first two months of this year, according to government figures, an annual rate exceeding 400 percent. Officials have promised new anti-inflation measures, but none has yet been taken.

Some analysts say inflation cannot be controlled until a new government takes power, with the authority to implement effective controls. "It is more a political problem," said Jacques Hirsch, the president of the Argentine Industrial Union. "This government cannot inspire confidence, it cannot create stable conditions, and as long as that is true some sectors will concentrate on trying to cover themselves" by continually raising prices.

Although the inflation-rate goal is not a mandatory standard of the IMF agreement, it could affect other measures that are, financial sources and diplomats say. High inflation could prevent the government from making the agreed-to real increases in utility and fuel rates or cancel the reductions in the rate of monetary expansion.

In addition, government officials have pegged both workers' wages and interest rates to keep up with the hoped-for level of inflation of 160 percent. With inflation running higher, salaries could be depressed and interest rates increased, creating recessionary effects--and political confrontations--the government meant to avoid.

By August, when the third $300 million installment of the IMF funding is due, some analysts believe that what is now a relatively comfortable financing program for Argentina will have changed. "This is a political year, in which an ordered policy like that planned with the IMF will be very difficult, for political reasons," said Hirsch. "The government will need to say 'no' to all sectors. But it may not have the strength to do that."