There are fears among some Green Party members that key areas in which they want to see "radical change", such as health and housing will be sacrificed due to concerns over the economy.
Housing was "parked" as a discussion topic last week after days of disagreement between Fianna Fáil, Fine Gael and The Greens, and Tuesday's discussion regarding the economy only furthered concern that issues on which Eamon Ryan's party campaigned heavily on will only see "small incremental changes", described by one TD as "kicking the can down the road".
Another TD agreed, saying: "There are a fair few issues with housing".
The disagreement has festered around funding for social housing and the department as a whole, the role of the Land Development Agency and the constitutional change suggested in the initial framework document put forward by the civil war parties.
However, the discussions around health "have been made easier by Sláintecare to be fair," the source said, "it helps every one to get on the same page".
The three parties are said to have found a number of areas of agreement around healthcare and the implementation of the programme.
Tuesday's talks on enterprise and green business initiatives however, were "hopeful", and pointed to progress towards a "circular economy".
The three parties also discussed initiatives to support SMEs, public finances while attention last night in a further round of talks turned to capital plans, particularly to help the country recover from the pandemic.
Fine Gael's Project Ireland strategy, including around infrastructure, broadband, and transport, was also updated. All these elements are expected to come under a national recovery plan, which was flagged by a joint Fine Gael-Fianna Fail framework document some weeks back.
Sources say that the Government is still committed to the Ireland 2040 capital spending plan, but that "pragmatism may take over" when it comes to deciding on the country's capital spending projects for the next two decades.
Both Fianna Fáil and Green senior negotiating figures last night were still hopeful a deal could be ready to present to all three party leaders some time next week.
However, agriculture policy for the new administration could be a last-minute stumbling block and has been left until then to negotiate
Meanwhile, some Green Party members have also flagged concerns to their parliamentary party about any future government involving controversial independent TDs Verona Murphy and Michael Lowry.
One prominent Green councillor said: "There has been a lot of disquiet that these people would be involved, it's disturbing and upsetting for us to be hearing and reading about it.
"The members would want some assurances before we go to vote that they will not be involving the likes of those TDs — those appointments are just not acceptable to us as a whole.
"I don't see the membership going for that at all, racism is a hard red line and a rubicon a lot of us wouldn't cross, given how strong we've been on it racism and the racism some of our members have suffered."