Fianna Fail leader Micheal Martin will face angry demands from TDs to allow them to serve in opposition after a disastrous general election.
The move could fast-track Mr Martin's resignation and trigger a leadership contest.
Brendan Howlin became the first senior politician to fall on his sword yesterday after he resigned from the Labour Party leadership.
Before he announced his resignation, Mr Howlin revealed Labour's six TDs would not be entering government during the next Dail term.
The decision significantly damages Sinn Fein leader Mary Lou McDonald's plans to lead a left-wing coalition.
Mr Martin is expected to tell a parliamentary party meeting today that he is opposed to entering into government with Sinn Fein.
This would leave open the door to Fianna Fail speaking to Fine Gael about a coalition which is supported by some in Mr Martin's party.
However, senior frontbench Fianna Fail TDs, including deputy leader Dara Calleary, Barry Cowen, Darragh O'Brien and Willie O'Dea among others, are opposed to entering into coalition with either Sinn Fein or Fine Gael.
Ruling out both parties significantly reduces the party's options, especially if Fine Gael will not support them through a confidence-and-supply agreement.
Ahead of the meeting, senior party figures were suggesting Mr Martin's almost decade-long leadership will come to an end sooner rather than later.
A number of TDs said even if Mr Martin manages to become Taoiseach, he will not lead the party into the next general election.
"There shouldn't be any need for a heave and Micheal must know himself that he will have to say when he is going, even if he's Taoiseach," a senior Fianna Fail TD said.
Another TD said: "At the end of the day he won't be leading us into the next election so he can go now or wait a year and go then."
However, others in the party were less eager for their leader to step down.
"No point in taking the captain off the pitch if you don't know who's coming on to replace him," a TD said.
Mr Martin has not spoken publicly since he left the door open to a coalition with Sinn Fein after the election.
However, party loyalists were yesterday suggesting Mr Martin was "buying himself some time" after the election.
Fianna Fail TDs have been getting a backlash from their supporters over Mr Martin's failure to rule out a coalition with Ms McDonald.
There is an expectation at the most senior ranks of the party that Mr Martin will rule out a coalition at today's meeting.
Fine Gael are also split on going into government with Fianna Fail.
Yesterday, Taoiseach Leo Varadkar said he expects to lead Fine Gael into opposition but also suggested there could be a second election.
"I think the likelihood is that at the end of this process that I'll be the leader of the opposition and obviously (if) my new parliamentary party still want me to do that, I will want to do that," he said.
However, some Fine Gael ministers believe they should approach Fianna Fail about forming a coalition.
But the Taoiseach's view is supported by other senior figures in the party.
Sinn Fein's negotiating team opened talks with smaller parties yesterday as Ms McDonald sought to form a government, with the Green Party and People Before Profit holding talks with the Sinn Fein team led by Pearse Doherty.