Recent opinion polls indicate Dutch voters will follow France in rejecting it.
Many Dutch voters say they fear a European wide constitution will create social problems and cost jobs - two of the reasons French voters gave for rejecting the pact Sunday.
Prime Minister Jan Peter Balkenende made a last ditch appeal Tuesday for a "yes" vote, saying a rejection would damage the Netherlands' reputation as a champion of European integration.
He has ruled out any political resignations if the Dutch reject the treaty. In France, Prime Minster Jean-Pierre Raffarin resigned and was replaced by Dominique de Villepin in the wake of the French "no" vote.
About 12 million Dutch are eligible to cast ballots in the referendum.
Preliminary results are expected Wednesday night.
Some information for this report provided by AP, AFP and Reuters.