Officials at the White House breathed a huge sigh of relief as a dissenting Democratic senator announced that he would vote in favour of the bill - supplying Mr Clinton with a crucial extra vote in the US Senate.
The decision, by the Arizona Senator, Dennis DeConcini, came after a tense day in which the President paid a last-minute visit to Capitol Hill in an effort to rally support for his amended plan. Few dispute that Mr Clinton has put his credibility on the line by repeatedly making clear that he regards the legislation as a central part of his agenda. Failure to get it through Congress would be a severe blow.
Mr DeConcini's vote is important because he was one of six senators who opposed an earlier draft of the bill in June, which the Senate only passed by a 49-50 majority after Vice-President Al Gore cast a tie-breaking vote. The six dissenters were subsequently joined by David Boren of Oklahoma, leaving the administration with the difficult job of winning over at least one of their ranks. Mr DeConcini may now supply the vote Mr Clinton needs - although a risk remains that senators who previously supported the plan may change their minds.
The main components of the package, which Mr Clinton has characterised as the first step in a historic attempt to reform government, are dollars 254bn ( pounds 170bn) in spending cuts combined with around dollars 242bn in new tax revenues. Most of the cuts will come from defence and by limiting the growth of Medicare, the government-funded health programme for the elderly.
The stakes rose still higher on Tuesday night when Mr Clinton made an impassioned, and rare, television address to the nation, brandishing bar charts showing that the great brunt of his proposed tax increases would be borne by the rich - and not the middle class. He claimed the only tax hike to affect most Americans was a 4.3 per cent per gallon increase on petrol.
Initial surveys suggest that the electorate was far from convinced. A USA Today/CNN Gallup poll taken after the speech found that only 33 per cent wanted the bill to pass. Nearly a quarter of those surveyed had no opinion at all, a sign that Mr Clinton's efforts to slay the deficit dragon has yet to remove public cynicism about gridlocked government.