The Greens and the Social Democrats say that the two traditional parties attempts to brief against them in the media will not help government formation.
Both parties have come under pressure and criticism from Fianna Fáil and Fine Gael to form a government in the "national interest".
Rumours of a divide within the Green Party over whether or not to go into government have been circling in the media for a number of days, which party whip Neasa Hourigan described as an attempt to create division within the party.
"There is a broad spectrum of political beliefs within the Green Party, but we are fully in agreement in our policies, and this is an attempt to disrupt that," she said.
Likewise, the criticism of the Greens has been noticed by the Social Democrats, who say they are aware that similar attacks are now coming their way as pressure to form a new government rises.
In the last day, Finian McGrath, the outgoing Minister of State for Disability Issues criticised the Social Democrats, saying the party were missing a "golden opportunity" to implement Sláintercare "their major policy, but the SocDems are missing in action at a time of national crisis.”
Sources within both parties, who have 6 (SocDems) and 12 (Greens) TDs respectively, say they have encountered "a level of arrogance" from the two majority parties, and a sense of "disbelief" that the progressive parties will not part with their principles for a place in cabinet.
Anne Marie McNally, the Social Democrats spokeswoman told the Examiner, that although the party are continuing discussions with all parties, the likelihood of her party forming a government with the two "civil war parties" is slim.
"We don't believe our policies are compatible with a Fine Gael and Fianna Fáil coalition, and it's not as straightforward as drawing red lines for what we want if we do enter coalition," she said.
After this health crisis, the government that will run for the next five years, in terms of compatibility and ideology, theirs is in stark contrast to ours, and it's hard to see realistically how we'd manage for five years.
"When we come out of this pandemic, we will have a changed economy and social environment.
"When it comes to deciding the economic realities we will be faced with, we have an entirely different worldview.
How six of us could fight against their policies and significantly influence them, is hard to see.
The deteriorating chances of either the Social Democrats joining a coalition leaves only Labour and Independents to make up the numbers needed for a majority coalition, as both Fianna Fáil and Fine Gael have ruled out working with Sinn Féin, who received the most votes in the election.
Sources within Fine Gael are said to be against the idea of relying on Independent TDs for government formation due to lack of stability.
Members of the Labour Party parliamentary party have held differing views on the issue. Leadership candidate Aodhán Ó Ríordáin previously said it would have to "one hell of a good deal" to get him to take the party back into government, Duncan Smith, the Dublin Fingal TD said he believes Labour should go into opposition and Cork East TD Seán Sherlock, believes the party should consider entering coalition.
Fianna Fáil leader Michéal Martin told TippFM on Tuesday that government could be formed within three weeks.
"Last week Fine Gael agreed to officially participate, so this week there will be exchange of documents, on how to reboot the economy and how we restore the country," he said.
"We believe we had good talks with the Green Party, they changed direction since those talks, it remains to be seen what other parties will participate.
"Once we get a framework document that will be the catalyst other parties can consider and engage in."
Mr Martin has come under pressure in recent days from some within his own party to look again at the Green Party idea of a national government.
Clare TD Cathal Crowe and Tipperary’s Jackie Cahill have both urged their leader to consider the idea.
Mr Martin was quick to dismiss the proposed all-party government, calling it “a recipe for indecision.”