For the President, who now has a fragile opportunity to begin turning round his administration's fortunes, the package's survival, by just 219 to 213 votes, was more a narrow escape from disaster than an enduring victory. Had it gone down, his whole domestic programme would have been in tatters. As it is, opinion polls show the President's popularity has reached a new low. The latest Newsweek poll shows his approval rating has fallen to 36 per cent. His standing in a similar poll at the end of April was 46 per cent and, less than two weeks after his inauguration, stood at 51 per cent.
The task is to preserve whatever fresh momentum he may now have to take on the Senate, where prospects for the budget bill always looked even more uncertain than they were in the House. There is a 57-43 Democratic majority among senators; but at least six Democrats are threatening to oppose the bill.
With about three weeks until the Senate is due to vote, the White House is preparing to bargain. While the bill survived the House debate with its principle planks more or less intact, protecting them in the Senate may prove to be much more difficult.
During this period, the President must also hope to avoid any more of the political calamities he has suffered over recent days and weeks. Events that have opened him to ridicule, ranging from his dollars 200 haircut debacle and the mess over the White House travel staff, undermine his authority and embolden those tempted to challenge him.
In a continuing, so far hardly fruitful, effort to regain popular support for the spirit of 'sacrifice' invoked at his inauguration, the President is packing for an extended road-show, especially in the states of wavering Senators. He made a start yesterday in Philadelphia.
The potential for further controversy looms on Monday, when the President is due to speak at the Vietnam Wall on the Washington Mall as part of the national Memorial Day celebrations. Mr Clinton, whose avoidance of the Vietnam draft was a hot issue throughout the election, is certain to face angry heckling from veterans who think he should not attend. But he has spurned advice to steer clear of the event.
The budget bill, aimed at beginning the process of pruning back the deficit, is a hard one for Congress to swallow, simply because it would mark the biggest tax increase in recent US history. As it stands, it contains dollars 240bn ( pounds 155bn) in tax hikes and nearly dollars 90bn in spending cuts over the next five years. Further spending cuts would be implemented at later stages.
Most at risk in the Senate is a proposed energy tax, which Mr Clinton appears determined to preserve as the most important revenue-raising instrument. But it is reviled by some Democrat senators who represent farming and oil-producing states that would be most affected.
The first hurdle is the Senate finance committee, where the Democrat majority is razor-thin, at just 11 members to nine. Among the Democrats on the committee is Senator David Boren, from Oklahoma, who has spearheaded efforts to sink the energy tax, which would cover all forms of energy consumption. An alternative now on the table, would call instead for an increased petrol tax only.
Some concessions on detail have been made by the White House. Exemptions from the energy tax have been offered, for instance, to the farming community and export rebates would be paid on energy-sensitive products. Mr Clinton also agreed a mechanism with the House of Representatives to ensure spending ceilings on federal welfare programmes.