Senior Green party sources said there was "considerable anger" at the lack of notice given to them by the Taoiseach yesterday about his intention to stand down as Fianna Fail leader.
It appears that anger could very well lead the junior coalition party to withdraw from government when they meet later today to consider the impact of Mr Cowen's decision to remain on as Taoiseach.
It is likely that even if the Greens did withdraw from government, they would vote in favour of the Finance Bill, given their commitment on it to date.
"The party has repeatedly stated its desire to get the Finance Bill through and even if the party does withdraw, party members are likely to support the Bill even if in the opposition," a source said.
Mr Cowen telephoned Green Party leader John Gormley just "a quarter of an hour" before he addressed the media in Dublin's Merrion Hotel, and informed him of his decision to step down.
At the press conference, Mr Cowen said that, following the week's events and after speaking to his family but acting on his own counsel, he decided yesterday morning that his position was no longer tenable.
He will remain on as Taoiseach until the general election on March 11.
Speaking to the media, flanked by Tanaiste Mary Coughlan and Chief Whip John Curran, Mr Cowen said: "I am concerned that renewed internal criticism of my leadership of Fianna Fail is deflecting attention from these important debates. Therefore, taking everything into account, and having discussed the matter with my family, I have decided on my own counsel to step down as leader of Fianna Fail. My intention now is to concentrate fully on government business and on continuing to implement the recovery plan."
At times, he seemed emotional as he read his statement, particularly when he spoke of his affection for the history and traditions of Fianna Fail.
"I have an abiding affection for the Fianna Fail party, its history and its traditions. I know the men and women of Fianna Fail, the length and breadth of the country are concerned about the party's prospects at the election. I too share those concerns," he said.
"I want the party to be in the best position possible to contest that campaign as a united organisation. At this crucial time, when decisions and choices have to be made, the focus should be on the policies the political parties are offering rather on the narrow focus of personality politics," he added.
Elsewhere, Fine Gael's Michael Noonan suggested on RTE News that his party would support the passing of all stages of the Finance Bill, but that the Government must go immediately.
His party leader Enda Kenny said it was utter and complete madness for Brian Cowen to resign as leader of Fianna Fail and remain on as Taoiseach of the country.
He said Fianna Fail was now a leaderless party in Government and he accused Mr Cowen of directly contradicting the position he had stated less than a week ago.
Mr Kenny said Ireland was now the 'laughing stock of Europe'.