Fianna Fáil leader Micheal Martin says it may not be "feasible" for party members to vote on the Fine Gael coalition.
Speaking on Today with Sean O'Rourke this morning, Mr Martin said that the next two to three weeks will be key in terms of forming a government, after the policy document agreed between his and Leo Varadkar's parties was published yesterday.
Traditionally, Fianna Fáil would require a vote by the party membership to approve such a coalition, unless the party's National Executive decided, by a two thirds majority, to bypass such a ballot.
A postal vote, like the process used for the Labour Party leadership competition, was suggested by local councillors as a way to ballot the membership while adhering to social distancing rules.
On an Ard Fheis, Mr Martin said: "That presents challenges with Covid-19, we will be engaging and consulting with all levels of the party, and we've already been doing that.
"All councillors were given the document yesterday, we'll speak to every single councillor in the country myself and the parliamentary party will be doing that, and likewise engaging with the membership on the ground."
When asked if he was considering a postal vote, Mr Martin said it would be "challenging".
"I don't think that's feasible at this stage, the rules state that usually there would be a specially convened Ard Fheis for a programme for government, Covid-19 rules out such large gatherings."
- Shop for essential food and household goods;
- Attend medical appointments, collect medicine or other health products;
- Care for children, older people or other vulnerable people - this excludes social family visits;
- Exercise outdoors - within 2kms of your home and only with members of your own household, keeping 2 metres distance between you and other people
- Travel to work if you provide an essential service - be sure to practice physical distancing
Local councillors and grassroots members of the party have already hit out at the lack of communication from the party headquarters over the possible coalition, with some elected members predicting that the party would attempt to avoid a membership vote as they did not believe it would pass.
"I wouldn't be surprised if they try to avoid an Ard Fheis altogether because they know that the membership won't go for this," one party representative told the Examiner.
Fine Gael and Fianna Fáil have both made it clear that they wish to see a third party join in the coalition, with the Green Party understood to be the preference for both parties, to make up their 72 seats to the 80 seats needed for a majority, and both are reluctant to rely solely on independent TDs, which they believe would not provide enough stability.
"The overwhelming view of the parliamentary party yesterday was to support a coalition with Fine Gael, that party members are aware of the unprecedented times we live in and the need to work towards forming a strong government to bring the country out the other side of the crisis," Mr Martin said.
"We believe a third party is the best approach... the securer the Government can be the better.
"This will depend on other parties and their approach to this, we've written to the leaders of other parties, Labour, the Greens and Social Democrats and asked them to engage, and the regional independent groups and other independent groups.
"We've already had good discussions with the Green Party and rural independents.
I can't preempt what the Green Party will do, it's very difficult for many politicians, I've always had a view that we have to accept the realities of an election and that demands that people have to engage and work to form a government.
"The point I would make is that sometimes a crisis presents an opportunity, and in climate change there is an opportunity here.
"In remote working for instance, that could have implications for public transport and traffic, there are opportunities here in terms of healthcare as well."
Some TDs have speculated that Ireland will not see a government formed until July, almost five months since the February election.
"The parties will need time, but the engagement should be about formation of government," Mr Martin said.
"One of the purposes of this document was to get things moving and stop informal discussions that were going nowhere, and it was the correct approach to take."
The framework document, which was maligned by critics and political rivals about the lack of detail and costing, is an effort to "get things moving", and Mr Martin believes it has created a focus and catalyst for engagement.
Sinn Féin's finance spokesperson Pearse Doherty said the document is basically "a wish list of vague promises" that contains no specifics but plenty of spin.
Speaking on RTÉ's Morning Ireland, Mr Doherty said the document does not tell us how many hospital beds will be re-opened or how many houses will be built and if Sinn Féin were to produce such a document, they would be "laughed out of it" by other parties and the media.
The document promises no tax increases or increases to USC, which many believe will be impossible as the country tries to recover from the pandemic.
"The framework document is a set of principles, and not a programme for government", Mr Martin said.