The emerging new White House approach, reported by several US papers yesterday, has not been finalised. The most obvious pitfall is resistance by Britain and other European countries, whose objections killed Mr Clinton's proposals earlier this year for punitive strikes against Serb positions and a lifting of the UN embargo on arming the Bosnian Muslims.
According to officials here, the administration is sounding out its allies. Mr Clinton himself declared on Wednesday that he was still weighing his options and would take no firm decision until the end of this week at the earliest.
But France, whose United Nations contingent in Sarajevo has come under shelling on several recent occasions, is believed to be shifting towards backing sterner steps against the Bosnian Serbs.
The officials say that no detailed soundings have yet taken place with Congress while the President himself, mindful of deep public unease at direct US involvement in the crisis in the ex-Yugoslavia, has made clear he would have 'appropriate conversations with the American people' before carrying out any important new departure in policy.
None the less, Washington is increasingly convinced that if anything is to be done, now is the moment. A determined stand on Sarajevo, Vice-President Al Gore, and Anthony Lake, his national security adviser, believe, would send the clearest possible message to the Serbs as the Geneva negotiations continue.
Mr Clinton himself concedes that limited action to protect UN peace-keepers may not be enough 'to deter aggression, to stop the shelling of Sarajevo, and bring the parties to the peace table'. But he continues to stress that any US action would only come in concert and agreement with its main Nato allies.
The new strategy being mulled over in the White House would represent the most significant escalation of US involvement so far. But there is no talk yet of sending US troops to help the UN on the ground, nor any sign that Washington will again press for removal of the arms embargo on Bosnia.
But many on Capitol Hill still favour precisely that.
Senator Richard Lugar, of Indiana, a senior Republican on the Foreign Relations Committee, said yesterday that air strikes and lifting the embargo could 'even up the sides' and produce real negotiation. Many Democratic Senators share that view.