there have always been problems with the political side of Europe.
First, it was only pure economical. In the 50s, they tried to expand the pure economical collaboration to a political union and a defense union. The political union did not receive much hail.
Trough the time, countries always were very hesitant of creating Europe as a supra-state. For economical matters, there was no problem. International trade is 'good' for every countries wealth. (soft matters)
On the other hand, the hard matters (defense, politics, justice) are the things a state is been dealing with since states first emerged. So on those matters, countries are certainly very hesitant of 'loosing' them.
But, the problem nowadays is the decision-making. Economic (and other soft issues) are delt with via the supra-national EU Commission: that is majority rule (a "government"). The hard issues are delt with via souvereign decision making (i.e. the countries come together as equals and they have to reach a consensus). A consensus means that it is VERY difficult to have an agreement. And so, it is slow.
Now we are with 25 and it is even more difficult to have a consensus.
Above all, nobody knows how the EU works
... there is a president for one year, there is the president of the Commission, there is a weak parliament, there is a kind of high representative... it's very heterogenous
THe constitution's main purpose is to create a new kind of decision making that is faster, more recognisable and more accountable.
ANd I think it's about time there is a new manner for decision making.
By the way, in France and in The Netherlands, most people didn't vote pro or con the constution. A referendum is a bad way: people probably vote against the incumbent government or against a person (prime minister).
edit:
http://www.europa.eu.int/constitution/download/brochure_160904_en.pdf