There is growing concern in Fianna Fáil that the long-drawn-out government formation talks are "running out of road".
The party wants the negotiations with Fine Gael and the Green Party to reach a conclusion in the next 24 hours so there is enough time for its 15,000 members to approve a government deal.
But as the talks drag on, key issues like the State pension age and the Green Party's demand to cut carbon emissions by 7pc a year remain unresolved.
The end of June has been identified by Taoiseach Leo Varadkar as a "hard deadline" for a new government to be in place due to urgent legislation that needs to be passed.
There is a belief among negotiators that a deal can be reached this week, but Fianna Fáil is particularly keen to get the process finished due to the logistical challenge of consulting with its members by postal ballot.
A party source said "it has to happen" for this reason and predicted that a programme for government will be agreed as the "vast majority" of issues are resolved. Their goal is to have the deal done so Fianna Fáil TDs and senators can consider it at a meeting tomorrow.
Another Fianna Fáil source said: "I still think a deal will be done this week, but we're running out of road in terms of getting it out to the members."
The unresolved issue of the pension age is said to be "rumbling along in the background", with the source warning "it's not going away".
Fianna Fáil wants the rise in the pension age to 67, due to happen next year, to be delayed pending a review.
This has been resisted by Fine Gael, which has been insisting on it being increased in line with a long-running strategy aimed at reducing State pension costs - albeit with a transitional payment for people until they reach 67.
There is a belief in Fianna Fáil that there is a "pathway" to reach a compromise on the issue.
The Green Party's key demand for a more ambitious yearly target of 7pc for cutting greenhouse gases may prove more difficult to resolve.
Negotiating teams for the three parties were last night understood to be thrashing out policies in the areas of agriculture and transport.
During a Dáil debate on climate action, Fine Gael Environment Minister Richard Bruton batted off questions related to the ongoing talks.
But he stressed the difficulty of measuring specific targets when Labour's Seán Sherlock asked for clarity on the Greens' 7pc demand.
Mr Bruton said his department had been looking at options to "dramatically increase our ambition".
He added: "As for saying there is an accurate way of moving from 3.5pc to 7pc or any other percentage, I do not think we are at that level of sophistication in the modelling at all yet."
He also said there will be challenges meeting targets in the new European Union 'Green Deal'.
"The reality is that we will probably end up in a position like Denmark, which has committed to high ambition but cannot specify all of the pathway.
"That is the reality we will have to follow," he said.
Fine Gael was last night said to be "determined to get a deal done" while acknowledging there was "still a lot of work to do". Among its priorities in recent days has been to ensure there is a jobs stimulus package in the first 100 days of government to help sectors like retail and tourism recover from the coronavirus shock.