Deliveries of Nice referendum literature could be affected if the pay dispute between the Irish Postmasters' Union (IPU) and An Post continues.
Rural post offices have refused to deliver publicity material as part of their industrial action which enters its fourth day today.
The IPU said the explanatory information, to be published by the Referendum Commission and delivered to every household in the State, could be affected by the dispute involving 600 rural independent post offices.
An Post, however, dismissed this and said the IPU was "grasping at straws".
The delivery of the referendum literature was "way down the road".
"A date for the referendum has not even been set."
Earlier yesterday, the managing director of post offices for An Post, Mr Eamonn Ryan, said in an interview that if the IPU wanted An Post to look at the system of payments he would be prepared to examine it.
However, the IPU dismissed the offer as "nothing new".
Mr John Kane, secretary general of the IPU, said this had been floated in the talks last week which broke down.
"It is just a euphemism for more delay," he said. "They have already had six months and are just trying to string it out."
He added that "there is no reason to look at the system but there may well be an issue about the value".
An Post "is prepared to investigate the whole postal system if we call off our dispute, but that would just delay things for at least another three months."
The dispute centres on payments for work carried out by the 600 independent rural postmasters and postmistresses who are sub-contractors for An Post.
The IPU says those sub-contractors have been paid €2 an hour for supervising and assisting with mail sorting.
Mr Kane said the postmaster or postmistresses in the post offices run directly by An Post are paid €21 an hour and this would €42 an hour before 8 a.m.
The IPU's members are refusing to start before 8 a.m, refusing to handle publicity or direct marketing material and refusing to handle returns on registered letters or parcels.
An Post has rejected the claims and said the IPU opted in 2000 for a "system of overall payments" rather than agree to a payment for individual activities, such as sorting of mail.
"They have already received a 12 per cent increase and a further 15 per cent in October and we feel we have dealt with them reasonably fairly. Now they want to go back to individual payments."
