Polling stations opened for the country’s 11.6 million voters at 7.30am (3.30pm AEST).
Recent surveys suggest almost 60 percent will vote against the treaty, triggering a last ditch appeal to vote yes by Dutch Prime Minister Jan Peter Balkenende.
“Let’s not let ourselves be led by polls,” Mr Balkenende told the TV program Netwerk.
“Let’s hope that when they’re in the voting booth, people think about all the people that say this constitution would be a positive development.”
He urged voters to support the constitution.
“I believe a no vote is not in the interests of the Netherlands nor in the interest of Europe,” he said.
“If you want to move the economy forward you must vote yes.”
But the prime minister’s support campaign for the yes camp may face a backlash as seen in France – some Dutch voters are expected to cast a protest vote against the government.
Resentment has grown over price hikes linked to the introduction of the euro three years ago, and many voters are concerned about Turkey’s bid for EU membership.
There are fears a ‘no’ vote would trigger a domino effect among European nations, with another founding EU member joining France in rejecting the document, which needs to be ratified by all 25 EU states to become effective.
However one pollster insists the French vote will do little to influence Dutch voters.
“People will do what they intended to do anyway,” said Peter Kanne from TNS Nipo polling.
TNS has predicted a no vote of 59 percent, with turnout below 50 percent.
Mr Balkenende has agreed to abide by the result if voter turnout is over 30 percent.