The worst of the neoliberal schemes European governments pursue in the mantle of the EU, the services-liberalising
Bolkestein Directive, became a threat to the EU project: despite all major parties' endorsement, a slight majority of the French public opinion turned against voting
"Oui" on the EU constitution.
To head off the shipwreck, the recent meeting of the EU Council decided to re-work the directive. I don't expect more than cosmetic changes, tough.
Should the EU Constitution be rejected by an anti-neoliberal, pro-social French majority, rather than an anti-EU, pro-"sovereignity" British majority, that could actually have positive effects: a re-drafting of the Constitution with more weight on social matters. (I'd be happy with strenghtening the parts on environment too, tough I don't see that happening due to a French
"Non".)
On the other hand. The weights in the Constitution, the near-unanimous support of states behind the Bolkestein Directive on services, and the software patents directive (actually another work of Bolkestein; held up only by vetoes of single states until the Luxemburg Presidency, there goes my respect for PM Juncker, pushed it through) shows the unfortunate fact that pro-business dogmatism is firmly implanted in the heads of nearly all the continent's major parties. So until that is changed[*], I will expect neither a much better Constitution, nor a better conduct of national governments with or without a Constitution of whatever nature possible at this time. (And, of course, without an EU, we would have zero common limiting regulation where we now have minimal.)
Hence, the neoliberal odour around the Constitution doesn't have much practical importance to me - the small increase in the European Parliament's powers, the small advance towards a common foreign policy and the big advance towards a fairer weighting of countries (after Chirac messed it all up in Nizza - which only got him the memorable Spanish-Polish blockade duo a year and half ago) matter more.
But everything possible should be done to defeat the Bolkestein Directive.
BTW, for those readers speaking German, taz has
some recent good articles on the issue.
[*] For the Left, the EU should be something to take over, not something to oppose as f.e. many in Sweden think. The Social Democrats wasted their time in the nineties when they dominated the EU-15, an example not to repeat.