But a schism between the pro- federalists and the Quebec nationalists at a special convention of his Quebec Liberal Party, a division highlighted when leaders of the youth wing walked out of the convention in disgust, will add to his difficulties in winning a referendum in October.
Polls taken since the basic principles of this latest attempt at rejigging the constitutional relationship between Quebec and the rest of the country were revealed about a week ago have indicated Quebeckers are almost equally divided into three groups: those for the deal, those opposed and those who say they do not understand it well enough to have an opinion.
The polls reflect the turmoil which has been going on in Quebec for the past two years since another attempt at amending the constitution, a set of proposals called the Meech Lake Accord, was blocked by some English- speaking provinces which did not like the special status it would have created for Quebec. It was also torpedoed by native leaders who said the rights of Indians and Inuit (Eskimo) were not sufficiently recognised.
This was seen by Quebeckers as an insulting rejection by Canadians in the rest of the country and support for separation into an independent country shot up.
Even though Mr Bourassa's Liberal Party is more federalist than the Parti Quebecois, which forms the official opposition in Quebec and is well ahead of the government party in the polls, the Quebec premier was forced to adopt a tough anti-Ottawa approach.
The Quebec government followed the advice of a prominent University of Laval political scientist, Leon Dion, who said that English Canada would only pay attention to Quebec's demands 'if it had a knife at its throat'. It demanded the federal government transfer exclusive jurisdiction to the province in 22 areas of government. As the Prime Minister, Brian Mulroney, responded, if the federal government had agreed to the demands, Ottawa would be left to deal only with the Queen and the national debt.
The compromise worked out in recent negotiations - the deal Mr Bourassa was defending at the weekend - recognises Quebec as a distinct society within Canada (a key condition of the old Meech Lake Accord) but transfers few additional powers to the province. Instead, it would give Quebeckers more influence within the national government including a large increase in representation in the House of Commons.
This leaves Mr Bourassa with a difficult challenge to convince the sovereignists in the province that Quebeckers' interests are better protected by more participation with the rest of the country rather than by more independence.
The new constitutional accord is still far from being a final deal. At the moment it is only an agreement between the leaders of the federal and provincial governments and native organisations.
To try to create political momentum to have it ratified, Mr Mulroney is considering holding a national referendum to coincide with the referendum already set for Quebec, although many of his advisers are urging caution.
They are afraid that voters may use it to express their disdain for Mr Mulroney or to protest against the favoured treatment they believe national governments have often accorded Quebec.