Questions have been raised over the exact cost saving that would result from the abolition of the Seanad.
In correspondence with the Referendum Commission a senior Oireachtas official said it is not possible to give an estimate of how much the move would save.
The claim that €20m will be saved by abolishing the Seanad has been central to the Yes campaign, and particularly so for Fine Gael.
Tonight it emerged that the Finance Officer of the Oireachtas informed the Referendum Commission that it is not possible to estimate the net savings that would arise if the Seanad is abolished.
The letter also states that a strong caveat has to be attached to the €20m figure, as this relates to costs that may not translate fully into savings in the event of the Seanad being abolished.
The €20m is made up of €2m in pension payments; €9.3m related to administration, IT and other costs, and just €8.8m is directly related to Senators' pay, expenses and their own staff costs.
In a statement issued tonight, a Government spokesman said: "The Government welcomes confirmation that the running costs of the Seanad are €20m per annum and acknowledge again that this figure, provided by the Oireachtas, is the only independently-validated figure for annual running costs.
"The Government believes that the money that could be saved following the proposed abolition of the Seanad would be far better spent in areas of more pressing need to people rather than on an institution that has proved itself to be unreformable.
"It is up to the Government to secure these savings and it is determined to do so."
Fine Gael director of elections for the Yes campaign Richard Bruton said: "We have a strong record in delivering on cost savings where rationalisations happen and are committed to delivering the savings in this case.
"Those on the No side seem determined to dismiss €20m as if it is not important and as if is not a lot of money; but the reality is €20m is enough to pay for, for example, 350 primary school teachers, or 1,000 new garda cars."
However, the letter's assertion that the net savings cannot be estimated is a setback to the Yes side, even though it insists the €20m can be achieved.
Meanwhile, Taoiseach Enda Kenny has been invited to take part in an RTÉ debate on the referendum on the abolition of the Seanad with Fianna Fáil leader Micheál Martin.
Both leaders have been offered an opportunity to participate in a debate on Prime Time next month.
Accepting the invitation, Mr Martin said: "I remain hopeful that the Taoiseach may yet realise the importance of a proper public discussion of his proposals."
Mr Martin added: "The only reason for refusal that the Taoiseach has given to date is his fear of causing me embarrassment. While that may well be the outcome of the debate, it is no reason to avoid having one in the first place."
RTÉ said it felt Prime Time could best inform the audience on the referendum with two shows of different styles, devoted to the subject.
The first programme, which involved a four-person panel, has already been aired and RTÉ has scheduled a debate on 1 October between, "the two leading political figures on either side of the campaign".