JUST TWO MONTHS ago, it was widely suspected in Washington that the Israelis wished to spin out the Lebanon talks indefinitely--to avoid having to come to grips with the Palestinian question. Serious people wondered, too, whether the new and fragile Lebanese government could put together a coherent negotiating strategy. These respective misgivings have since been somewhat eased. But the latest American consultations with the foreign ministers of the two countries, here in Washington, indicate that the going is still very slow.

Lebanon seems ready. The government realizes it has a historic but perishable opening to rid Lebanon of its foreign occupiers, especially Syria, which is the real long-term threat to its independence. Lebanese authorities will not say out loud that the Israeli invasion created this opportunity, but plainly they do not want to waste it. They see working with the United States to end Israel's occupation as their only way also to end Syria's and the PLO's. They cannot be expected to accept the gross infringement on their sovereignty--a semi-permanent Israeli military presence--that Israel is demanding, but in their weakness they seem ready to accept a temporary lesser infringement.

In Israel, the public is losing its tolerance for the army's continuing casualties and costs in Lebanon, for the thankless task of pacifying Lebanon's warring factions, for the new military risks associated with Syria and for political strains with Washington. These burdens have led Israel to soften its negotiating stance to a point, thanks largely to Moshe Arens' replacement of Ariel Sharon as Israeli minister of defense.

Mr. Arens is a tough egg. He lacks his predecessor's large personal need to justify the Lebanon operation by pursuing extravagant goals, such as the recasting of Lebanese politics in a form akin to the partition of Lebanon. With Foreign Minister Yitzhak Shamir, he is giving priority now to ensuring border security. But the key question remains whether they see the wisdom in not imposing upon the Lebanese the sort of outsized political burden under which Beirut will collapse.

The Lebanese yearn for an agreement. Other nations, not least the United States, have important peacekeeping and steadying roles in bringing one about. But the Israelis' attitude is crucial. If they can refrain from overreaching, and thereby weakening the very Lebanese government they say they want to strengthen, an agreement may still be possible.