The EU expansion brought 10 new countries into the fold, most of which have economies closer in price structures to the Third World than to their West European neighbors.
Membership means that the easterners' skilled but cheap labor, and lower operating costs, are now on offer within the EU itself. And that has lured manufacturers and investors away from high-cost Western Europe.
As the French referendum campaign has gathered pace, the groups calling for a "no" vote have multiplied. Some are more serious than others, but one theme has remained constant, namely that the new constitution is "ultra-liberal" in economic terms and will end up undermining the elaborate French welfare state.
Contained within that idea is fear of the challenge from the east -- a challenge that will likely grow as ever more eastern countries press for EU membership.
Senior Research analyst Philippe Moreau de Farge, of the French Institute of International Relations in Paris, says this is one key reason why the French people have never accepted the EU expansion. The expansion was never put to a referendum in France, but was decided on by political elites.
"Enlargement has not really been accepted by the population, it's clear that in the French population, many people are not happy with enlargement, and consider that enlargement has been imposed, has been dictated, and was not a free choice of Western Europe, and especially of France," Moreau de Farge said.
As the referendum campaign in France moves to a climax, the "no" vote has the momentum, but all will depend on the voters who are still undecided. Both the pro and anti-constitution factions want a high turnout.
Turning to the Netherlands, we find a different mix of factors that may bring a "no" vote on 1 June.
The Dutch were regarded for decades as staunch integrationists, but the latest opinion polls cast doubt on this. Dick Leurdyk, senior researcher at the Netherlands Institute of International Relations, says the apparent turnaround is remarkable.
"We have been seen by others and we have seen ourselves also, as strong supporters of the European unification process, and now indeed with a focus on this [constitution] ratification process, that seemed to change, and I must say I am a little bit surprised," Leurdyk said.
Leurdyk points to various, rather vaguely expressed reasons for rejecting the document. These include factors like fears of losing the Dutch identity, concern that the country's ultra-liberal drugs laws will be curbed under EU law, and worries that if Turkey is admitted to the union, there will be an immigration flood.
The Netherlands has in recent years made economic adaptations to face globalization, and fear as in France of the economic aspects of the EU's eastward expansion is not considered an important factor.
So what will happen if the French or the Dutch, or both, reject the constitutional treaty? French officials have issued dramatic warning about the paralysis in the 25-nation EU. But these can be seen as partly exaggerated.
The EU has a long tradition of muddling through, and it would presumably continue to do so in the future, although this would reduce its effectiveness as a political player on the world stage. And further expansion eastward could be put in doubt. Romania and Bulgaria can count themselves as in, but prospects for big applicants like Ukraine and Turkey would appear more uncertain.
Marcus Vahl, senior analyst with the Center for European Policy Studies in Brussels, says if there is a "no" vote either in France or Netherlands, or in any of the other referendums that are coming up, the EU would probably seek to incorporate chunks of the constitution into its present rule book.
"The idea now is that if there is no constitution they would try to get at least some of the parts [of the constitution] operating, in particular the post of foreign minister and the external affairs service, or perhaps get a [complete but limited] new deal that does not require ratification, or voting," Vahl said
EU officials have said there is no Plan B to fall back on if the constitution is rejected. But analyst Vahl says that in the case of the Netherlands in particular, it's possible the government could decide to hold another referendum on the same issue next year.
That method has been successfully used previously in Ireland and Denmark to pass treaties, although some people disapprove of what they see as a technique to continue voting until the public give the "right" answer. All EU members must approve the constitution before it can come into force.