The King's unusual solution was to appoint Mr Dehaene to mediate a compromise between the four coalition partners. The job is more usually accorded in such situations (there have been several) to someone outside the immediate dispute. But by selecting the Prime Minister, the King gave Mr Dehaene the flexibility he needed to persuade the coalition that its very survival depended on a compromise.
Faced with agreed budget cuts of 110bn Belgian francs (pounds 2bn), the coalition could only agree on reductions amounting to Bf75bn. The French-speaking Socialists refused to sanction limitations on the custom of index-linking salaries, while the Flemish-speaking Christian Democrats refused any further attacks on the family allowance. The problem has been solved by leaving both elements out of the budget package. The necessary savings will instead be found by privatising certain state assets and through more rigorous accounting, including a crackdown on fraud and tax avoidance.
The deal done, King Baudouin announced last night that he would not accept the government's resignation - a device which now allows the coalition to continue in office unchanged.
A government spokeswoman confirmed last night that there would be no changes to the cabinet, which groups Socialists and Christian Democrats from both the French and the Flemish regions of the country.
With the budget crisis averted, Mr Dehaene is now free to concentrate on pushing through parliament the constitutional reforms with which he hopes to claim his place in Belgian history. The legislation now in train, which should be approved by July, will devolve significant power to the regions, creating a fully-fledged federal state.
The reforms are designed to answer the growing demand for autonomy from prosperous Flanders, which feels its economic contribution to the country is not matched by political clout.