THE MEXICAN debt negotiations now going on here will set influential precedents for all the other Latin debtors. The Mexicans are pressing hard for concessions, but not so hard that they jeopardize the negotiations. The United States government and the commercial banks are resisting, but not so hard that they ignore the limits to Mexico's ability to pay.

The price of oil dropped precipitously in January, and in early February Mexican officials told their bankers in New York that, to meet their debt commitments, they would have to have new loans on a far larger scale than previously anticipated. Mexico would need $8 billion to $9 billion in 1986, they said. The United States government reacted with exasperation, objecting that the Mexicans were using exaggerated figures and setting off ripples of anxiety among the banks.

Later in February the president of Mexico, Miguel de la Madrid, declared in a televised speech that Mexico's payments on its gigantic debt must be limited "in accordance with the country's ability to pay." That, he said, would require "sacrifice" on the part of the lenders as well as Mexico; the debts can't be managed solely by austerity in Mexico. The following week Mexico's minister of finance, Jesus Silva Herzog, spent several days here in Washington in conversations with the Reagan administration. They ended, apparently, with agreement that there was no need after all for emergency aid. The Americans argued that Mexico could manage with the $6 billion of new financing that had previously been arranged. As the Americans saw it, Mexico wanted the additional billions not to service foreign debt but to avoid having to cut its domestic budget.

To make the debt burden more easily bearable, the most effective remedy would be to attract private capital into Mexico -- above all, some of the billions of dollars that wealthy Mexicans sent abroad in the great waves of capital flight earlier in this decade. To draw that money back into Mexico will require economic stabilization, beginning with reduction of the budget deficit. It's been running about 10 percent of GNP -- in relation to the size of the economy, twice the size of the current budget deficit in this country. But cutting the deficit is just as hard in Mexico as it is here, and for the same kinds of reasons.

Last week the governments of the indebted Latin countries met in Uruguay to discuss joint strategy, but the conference ended inconclusively. The Mexicans were unwilling to take any position that might interfere with their own negotiations. But the meeting was clearly inclined to favor a demand for cuts in interest rates -- even cuts well below market rates.

That's an unattractive idea from the point of view of the lenders in the United States, Europe and Japan. It means subsidizing the interest on the Latin debts, and if the commercial banks are forced to do it the costs will be widely spread across the world economy in the form of higher rates for borrowers in the industrial countries.

Today Mr. Silva Herzog returns for further talks at the Treasury. These negotiations are far from ended. But the decline of interest rates in recent months has somewhat lightened the debtors' burden. The case for subsidized interest is not yet persuasive.