Amid speculation about a US request to Russia to mediate and the imminent release of the captured US servicemen, Mr Clinton said: "We are determined to stay united and to persist until we prevail."
The truce proposed by the Yugoslav President was unacceptable: "It is not enough for Mr Milosevic to say his forces will cease fire in a Kosovo denied its freedom and devoid of its people ... He must withdraw his forces, let the refugees return, permit the deployment of an international security force."
As members of his immediate team are criticised for their handling of the crisis - not a day goes by without some disclosure about errors by the Departments of State or Defense, or the military - Mr Clinton ploughs on and his efforts seem to be paying off. His ratings for handling the operation have improved and opinion has hardened substantially: against Slobodan Milosevic, for the military action and for deployment of ground troops.
A Wall Street Journal poll showed 64 per cent approving "US and Nato air strikes". Asked if they would "favour or oppose sending US and Nato soldiers into Serbia if the Serbs continue to drive people out of Kosovo", 53 per cent said they would approve.
When the question was put more starkly - would they approve sending US and Nato soldiers into Serbia if that was "the only way to stop the fighting" - the proportion rises to 73 per cent in favour. This is an almost 30 per cent increase in Americans who would support deployment of US ground troops since air strikes began. It brings the US much more into line with European - at least north European - opinion.
A similar shift has been seen among opinion-formers - policy advisers, academics, military experts and politicians. Determination to "finish the job", if necessary with ground troops, has changed from hesitant acceptance that this might be the only option into a crescendo of support.
The upshot is that Mr Clinton, who yesterday continued to insist through cabinet members that there were no plans to use grounds troops, could find himself contemplating a policy U-turn by popular - and congressional - acclaim.
If this happens, he will have to thank the disarray on the right. Aside from a small group of conservatives, led by Pat Buchanan, who have said from the outset that no US interests are at stake in Kosovo, the majority have twisted and turned through a series of misjudgements to the point where they are lined up, more or less, behind the toughest possible line on Mr Milosevic.
Senator Don Nickles, a senior Republican who had reportedly said he would not support military action until "the Serbs started massacring people", was embarrassed into saying he was quoted out of context. It is said he would now vote for ground troops and take the vast majority of Republicans into the lobby behind him.
Even a recent call by William Odom, former head of the National Security Agency and respected military strategist, to "Take Belgrade" does not faze them.
Much may have gone wrong in the Nato operation for Kosovo, but for Mr Clinton almost everything has gone right.