It was the second referendum defeat for the treaty in quick succession after France voted to nix it on 29 May.
A downcast Jean-Claude Juncker, the prime minister of Luxembourg, the current EU president, appeared to question further EU integration, observing: "Europe no longer makes people dream."
Jose Borrell, the president of the European Parliament, also offered an emotional explanation, blaming the various fears of the Dutch electorate. But he appeared to share the view of the EU presidency and European Commission that ratification must continue.
"Fear was stronger than the dream. And in these moments, what needs to be done is for all Europeans, all the countries, to have the opportunity to express themselves, as predicted at the time of signing the constitutional treaty. We give the French and Dutch vote a lot of importance, without a doubt. But we must also give a lot of importance to the other Europeans," Borrell said.
Various EU leaders have repeatedly this week appealed for calm, calling for a period of "reflection" until the scheduled summer summit in Brussels on 16-17 June.
Jose Manuel Barroso, the president of the European Commission, after the Dutch vote called on EU member states to defer any decisions until the summit.
"I think that we must ask all member states to refrain from taking unilateral decisions at this point and before the European Council. Although it is important to find a consensus, I salute the Council Presidency's initiative to dedicate part of the next European Council to analyze this problem, which is a serious problem. For our part in the Commission, we are determined to continue with our program," Barroso said.
The immediate object of Barroso's plea for time is Britain, where officials have indicated they are considering suspending legislation that would allow for a referendum on the constitution to be held in early 2006.
Such a suspension of the British referendum could be announced next week, but it would be couched in terms that make it clear that the measure represents only a temporary halt -- and not the abandoning of referendum plans altogether.
Most other EU member states have reconfirmed their intention to continue with ratification. Today, Latvia became the 10th member state to ratify the treaty.
However, EU politicians and analysts are keenly aware that the tide of public opinion is turning against the constitution and future referendums will be increasingly hard to win -- and their fallout increasingly more damaging.
Dick Leurdijk, a researcher with the Netherlands Institute of International Relations, says the EU is close to where it must decide whether to hold any more referendums.
"I think the first question that now has to be answered is, 'Shall we go forward with the ratification process? Yes or no?' And only after we have decided on this issue, then other issues can be discussed as well. Because [the question of what can be salvaged from the constitution] suggests that we will find ourselves in a kind of negotiation environment. And at this moment, we are not yet that far," Leurdijk said.
Another analyst, Philippe Moreau de Farge of the French Institute for International Relations, tells RFE/RL he believes the summit will quickly agree to look for alternatives to having the full constitution ratified.
"I think there will be, very quickly, a negotiation to find an alternative solution and, probably, the alternative solution could be a limited treaty including some elements of the draft constitutional treaty, for instance, maybe the (EU) Foreign Ministry, maybe the new rule for qualified majority voting, maybe the permanent president for the European Council," Moreau said.
Leurdijk partly disagrees. He says a final decision on the constitution can wait. He suggests a longer time for reflection may be necessary before any further moves toward EU integration.
"Our fallback position would be to continue along the lines of the (EU's) Treaty of Nice, and we could continue to do that for a couple of years and then, in the meantime, ask ourselves what to do with the constitution. And I think we should take the time now to reconsider the situation and to ask ourselves whether it has been a good idea to come forward with this constitution, as such," Leurdijk said.
At this point, the future of the constitution hangs very much in the balance. One of the very few clear things to emerge from the past few days is that Brussels was caught off guard by the French and Dutch results and this time genuinely does not have a "Plan B" for the EU.
(RFE/RL's Bruce Jacobs contributed to this report)