By Stephen Mulvey
Luxembourg votes on Sunday in what will be the last referendum on the EU constitution this year, and could be the last ever.
Luxembourg does not want to sound the death knell for the treaty
"If this country says 'No', then according to my colleagues in the European Commission, this would clearly mean the treaty would be dead," Prime Minister Jean-Claude Juncker has warned voters.
He has also threatened to resign, bringing to an end 11 years in power.
A poll conducted last month, after the rejection of the constitution in France and the Netherlands, suggested that 46% of Luxembourgers were in favour and 38% were opposed.
In October 2004, the corresponding percentages were 60% and 19%.
No polls have been allowed since the June survey.
Correspondents say rallies organised by the "No" camp have been well attended, while the major political parties - which all back a "Yes" vote - have struggled to attract big crowds.
But Foreign Minister Jean Asselborn said on Wednesday that the rise in support for a "No" vote had stopped and the undecided voters were now leaning towards a "Yes".
He also suggested that a "No" vote in Luxembourg would turn the country into the constitution's "undertaker".
Since the end of Luxembourg's EU presidency on 30 June, Mr Juncker has been active on the "Yes" campaign trail.
As in France, opponents of the constitution have argued that it would lead to sweeping free-market reforms.
Jean-Claude Juncker has threatened to resign over the result
"We do not want a treaty that dictates its ultra-liberal orientation, with completely free competition, with liberalisation and privatisations," a co-ordinator of the "No" campaign, Anne-Marie Speltz, told AFP.
Mr Juncker has countered by reassuring voters that the constitution will not affect the country's labour laws, or lead to any change in its low rate of VAT.
"Yes" campaigners have also been at pains to emphasise the benefits that EU membership has brought the country.
"In 1952 we were the poorest country, now we are the richest one," Jacques Santer, a former Luxembourg Prime Minister and President of the European Commission, has been quoted as saying.
Some voters have complained about feeling blackmailed by Mr Juncker's threat to resign.
Yes or No
However, correspondents say the prime minister's tireless, but ultimately unsuccessful, attempts to negotiate a deal on the EU budget at the 16-17 June summit in Brussels have won him the public's sympathy.
The question being asked, in three languages, is: "Are you in favour of the treaty establishing a constitution for Europe, signed in Rome on 29 October 2004?"
Voters can answer either "Oui" or "Non" (French), "Jo" or "Nee" (Luxembourgeois) or "Ja" or "Nein" (German).
Until the French and Dutch "No" votes, a rejection in Luxembourg would have been considered scarcely conceivable.
The country is one of the six founder members of the EU, and the home to a number of EU institutions.
Mr Juncker even argues, tongue-in-cheek, that Luxembourg is a major beneficiary of enlargement, as it is no longer the smallest country in the EU, its place having been taken by Malta.