Fianna Fáil TD and former minister Mary O'Rourke has called for a special meeting on the leadership of the party in the new year and said people should be given a chance to "throw their hats in the ring".
She made her comments at a meeting of the parliamentary party this evening, according to people in attendance.
Earlier Minister for Tourism Culture and Sport Mary Hanafin signalled for the first time her willingness to stand for Fianna Fáil leadership.
Speaking before a tourism conference in Dublin, Ms Hanafin said she would "throw my hat in the ring" if the parliamentary party wanted her to.
However, Ms Hanafin said that would only happen in the case that there was a vacancy. "That could be a long way down the road," she said.
She said there was no indication of a heave against Taoiseach Brian Cowen and she would have no part in it if there were. She also stressed that the “whole concentration” of the Government should be focussed on getting the budget through the Dáil.
Ms Hanafin added that she was “very annoyed" by the Green Party’s surprise decision to call for a general election next month. “I am not sure that they have shown that they have the best interests of the country at heart but we are just going to have to work with them over the next few months," she said. "This is bigger than the Green Party and bigger than Fianna Fáil."
Last night Mr Cowen announced there will be a general election early in the new year once the budget has been enacted. His decision to dissolve the Dáil in the new year came in response to an announcement by Green Party leader John Gormley in the morning that his party wanted an election in the second half of January.
Several backbench Fianna Fáil TDs who believe it is time for the Taoiseach to step down are due to meet today to discuss “a strategy in relation to a motion of no confidence”.
Cork North Central’s Noel O’Flynn said tonight’s parliamentary party meeting would be a “bare-knuckle” affair and he would be calling for Mr Cowen to resign.
“I felt humiliated, frustrated and betrayed by not having known last week and the reason why the Greens have pulled out of Government is because they were kept in the dark [on the bailout] as well,” he said.
Dublin South TD Tom Kitt said the people needed to be told exactly why the Government was doing what it was doing and how it proposed to implement the four-year plan.
“I think for whatever reason he [Brian Cowen] hasn’t done it and I believe for that reason that we need a new leader going into the next general election,” Mr Kitt said.
Dublin North TD Michael Kennedy said at the meeting he will ask the Taoiseach “why the events of last week happened, what his plans are for the future and if he considers himself the best man to lead us into the next election”.
Mr Kennedy said although there was speculation surrounding a motion of no confidence in Mr Cowen ahead of tonight's meeting he said he had not been asked to sign anything but he would if asked.
Carlow Kilkenny TD John McGuinness said: “There’s serious discontent within the parliamentary party. I believe it’s now up to those who’ve spoken out to take soundings amongst their colleagues to take action to remove that man [Mr Cowen] immediately,” Mr McGuinness said.
If a strategy was agreed, it would take a week for a motion to be heard.
Today Limerick TD Niall Collins said internal Fianna Fáil politics needs to be “parked” for the time being in the long-term economic and financial interests of the country.
“We have to separate the domestic political positioning that’s going from the larger and much more important international picture which Ireland needs to deal with at the moment.”
Mr Collins said he did not feel any challenge to Mr Cowen would be able to obtain the required 18 signatures needed to put the party leadership on the agenda at tonight’s meeting.
“The whole issue of who leads Fianna Fáil is not the issue at the moment,” he added.
Galway West TD Frank Fahey said he has confidence in Mr Cowen and that the “important thing now is that we deal with the budget and the four-year plan and we put those measures through the Dáil to avert a more serious crisis”.
Mr Fahey also added that he felt the way the Greens announced their decision to leave Government was “a little bit disappointing”.
Earlier on his way into a Cabinet meeting Minister for Finance Brian Lenihan said the priority for the country is the budget and that the Taoiseach will lead Fianna Fáil into the next election.
“We need to pass this budget we need to publish our plan tomorrow which we will be doing, the plan has been finalised the budget will be introduced and the necessary funding for the budget will be obtained.”
"They are the priorities for this country at present.”
Minister for Transport Noel Dempsey said the easiest thing for Fianna Fáil to do would be “to walk away from this, to have an election, to allow somebody else come in, and wash our hands of the whole things.”
But he said the EU-IMF rescue deal for Ireland hinges on the publication of the four-year plan and the passing of the budget on December 7th.
"We don't have the luxury of time in relation to this. We asked for assistance, we were given that assistance on the basis that we were going to produce this four year plan, that we were going to produce a budget, and that that budget would pass," Mr Dempsey said.
"If we can't do that, then the assistance isn't there."
“The proper thing for the Opposition to do is put the country first, put aside politics as usual and get on with this business,“ he added.
Mr Dempsey also said the Taoiseach Brian Cowen will lead the party into the next election.
"Brian Cowen has my full support now and into the next election," he told Morning Ireland.
On the same programme Dan Boyle of the Greens said his party had decided to pull out of Government because of the “feeling of distrust” among the ruling parties.
“We feel that there has been unnecessary confusion caused by how that [bailout negotiations] was communicated by our partners in Government and that’s one of the sources of our unhappiness,” Mr Boyle said.
He said the party will remain in the Government because there is a “critical job” to be done over the next couple of months.
“After that we believe there is a need for a general election and that seems to be an analysis that is shared by our partners in Government.”
Mr Boyle said it would be impossible to hold an election immediately because it would mean a delay of several months to implement the budget “at a crucial time of our political and economic history”.
“We say that the next two months have to be dealt with collectively, not only by the parties of Government but by all political parties, get us over this period and then have an election,” he added.