But the problem now is that the document must be approved by each member state. And some of the most skeptical members, such as Britain and Denmark, have decided to hold national referendums on the issue. In the opinion of many, such referendums are practically unwinnable, given the present state of public opinion.
The senior political commentator of Sweden's daily "Svenska Dagbladet," Anders Junnson, says the basic reason for the public disquiet is that the European Union has never been able to define its own endpoint.
"If you look at the history of the Union it is always like this, they go further, then they stop, and then they go back, and really the reason for all this is the [unanswered question] of what is the European Union -- is it a form of cooperation among sovereign states, or is it going to be a federation? That is what it is all about," Junnson says.
The philosophical divergence between those two schools of thought, which has been rumbling for years, appears to be coming to a head in the events surrounding the constitution.
Those who prize their country's sovereignty above all else reject the constitution for what they see as the ever-growing centralization it imposes on the way toward a federal state.
Those who favor an increasingly strong union, on the contrary, see the document as actually limiting the flow of political power to the center because it defines the exact role of authorities in Brussels.
Junsson says that in view of this incompatibility of outlook, there is a "great risk" that the EU will soon lose the cohesion which has been built up over the last half-century.
"[As to] what the Union is going to be, it appears that some countries could move ahead, and develop more cooperation, while other [countries] will not do that, so of course we would then have a Union which is not all that tied together," Junnson says.
Another analyst, Antony Kaminski of the Institute of Political Studies in Warsaw, agrees that Europe must develop a "clear idea" of the direction it should take. He points to the value of integration, in that if the European project falls apart, there could be a return to balance-of-power politics in Europe -- a system which proved disastrous in the war-ridden 20th century.
But Kaminski says that even if the constitution fails to win ratification, that would not necessarily be disaster, in that Europe as an idea is still evolving.
"Europe is a moving project, we should all the time discuss the basis of European integration, and in discussing the basics, we should treat this as an open-ended project, so I don't think [a failure of the constitution] would be a tragedy," Kaminski says.
But that may still spell practical troubles for the union, according to Sweden's Junsson. May's massive eastward expansion of the EU by 10 new members means the old EU institutions are barely able to work efficiently. Without the streamlining of decision-making foreseen in the constitution, the union will be struggling to implement coherent policies.
Of course, the constitution may achieve ratification by all 25 members, which would at least temporarily blunt the philosophical debate and allow the expanded union to work efficiently.
Britain is seen as the most difficult referendum to win, with media polls this weekend indicating a majority opposed to the document. Voter sampling done for the weekly "The Sunday Times," for instance, indicates 49 percent oppose it, and 23 percent support it. Prime Minister Tony Blair has already opened his campaign to gain a "yes" vote in a referendum possibly next year.