The proposals had been developed through months of intense negotiation, but several of the most senior federal cabinet ministers attacked both Mr Clark and the proposed deal during a day-long meeting on Wednesday.
A special session of Parliament that was supposed to begin on Wednesday to discuss the deal was cancelled while Brian Mulroney, the Prime Minister, who was noticeably reticent about the compromises struck by Mr Clark, tried to find a new consensus.
Among the most contentious issues are proposals to turn the appointed Senate, or upper house, into an elected body with powers to block or delay federal legislation, and a scheme to give Canadian native peoples a measure of self-government.
Quebec's Premier, Robert Bourassa, has been boycotting the talks, arguing that it is up to the rest of the country to make Quebec an offer to replace the Meech Lake constitutional accord which failed to be ratified two years ago.
Failing an acceptable offer from the English-speaking part of the country, Mr Bourassa intends to hold a referendum in Quebec next October on the question of sovereignty or independence for Quebec. But he is now indicating his willingness to meet informally with other premiers and the federal government to modify the tentative agreement.
Last month, Mr Clark emerged from meetings with provincial premiers with an apparent agreement that would give all provinces equal representation in a new elected Senate, regardless of size. This had been demanded by several of the smaller provinces, such as Alberta and Newfoundland, as their price for agreeing to a wider constitutional package including the recognition of a special status for Quebec. The package would also restore a number of other conditions that would have applied to Quebec had the Meech Lake accord been ratified.
But giving a tiny province like Prince Edward Island with 100,000 residents the same representation in the Senate as Ontario with 9 million people would mean a massive reduction in the relative influence of the most populous central provinces, especially Ontario and Quebec.
Because of Quebec's hesitant response to the Clark deal, and Mr Mulroney's commitment that no amendments will go forward without Quebec's approval, the situation is now in flux.
Meanwhile, several federal ministers said proposals to shift powers and responsibilities to the provincial level of government (as demanded by Quebec) would so weaken the federal government's ability to manage the economy that it would become ineffective.
Ironically, the only group that appeared pleased with the tentative deal were representatives of indigenous Indians and Inuit, who effectively scuttled the Meech Lake Accord two years ago.