Fine Gael last night demanded that Mr McCreevy resign following the news that Mr O'Flaherty had withdrawn his name for the post of EIB vice-president.
Mr Michael Noonan, the party's finance spokesman, said only the resignation of the Minister for Finance would show the public that the Government understood the principle of ministerial accountability.
"Responsibility for this fiasco rests squarely on the shoulders of the Government, but particularly on the shoulders of the Taoiseach, Bertie Ahern, the Tanaiste, Mary Harney, and the Minister for Finance, Charlie McCreevy," he said.
Mr Noonan accused the Government of leaving Mr O'Flaherty "to swing in the wind" when it became clear that the nomination might not win the necessary support.
"This behaviour is totally in line with the previous practice of the Taoiseach where members of his Government and his party, despite guarantees of support from him, became scapegoats and fall guys once they found themselves in difficulty, while Mr Ahern rode untouched off into the sunset," he said.
"Now that Mr O'Flaherty has withdrawn his name for consideration by EIB, the Government owes the Irish public a full explanation of why this was done when only a year ago they were moving to impeach him."
He said there must be a full sworn inquiry where all participants could be examined under oath.
The Labour leader, Mr Ruairi Quinn, said Mr O'Flaherty's decision was "the right thing under the circumstances".
He blamed the Government for putting Mr O'Flaherty in such a difficult position.
"In a breath-taking display of arrogance and incompetence, the Government chose to ignore the verdict of public opinion about the O'Flaherty appointment and in the process put Mr O'Flaherty and his family in an invidious position."
Mr Quinn said the credibility and political judgement of the Government were in tatters.
"Our reputation and standing in Europe have been damaged, European institutions have been tarnished and public confidence in the political process has been further eroded by the arrogance of this Government," he said.
Mr Denis Riordan, a lecturer at Limerick Institute of Technology who brought a judicial review against the Government over its decision, said Mr O'Flaherty's withdrawal came too late.
"He should have done it long ago; he is only taking the decision now to rescue his credibility."
He said this week he would apply in writing for the EIB post and would be watching to see how the bank dealt with his application.
"There are still questions about the procedures the bank uses to choose people for these posts and by putting in my own application I will be able to see what they are doing."
He added: "I am applying for that reason but also hope to get the job. I could do with £147,000 a year and unlimited expenses."
He understood 16 applications had been submitted to the EIB for the post and he said the 16 had a right to have their applications properly considered.
"I wrote to the EIB on August 15th asking them what qualifications were required for the post, I have received no reply. So they have no right to come back to me later and say I am not qualified."
He said if the Government decided to nominate another candidate it would, in accordance with the recent Supreme Court judgment, only be expressing a wish. "It would have no legal validity," he said.
Senator Helen Keogh (FG) welcomed Mr O'Flaherty's decision to withdraw his nomination but said it was "far, far too late".
Ms Keogh left the Progressive Democrats in June to join Fine Gael, citing the Government's decision to nominate Mr O'Flaherty as the deciding factor in her quitting the party.
Last night she said the whole issue was a grave embarrassment to the Government. She said the decision vindicated her opposition to the nomination. "I feel that it is the right thing for him and the right thing for the country. I've nothing personal against Hugh O'Flaherty. He is a fine man with very fine qualities but this was the wrong decision from the start."
She said she did not blame Mr O'Flaherty for the problems which arose following his nomination. "I would lay a lot of the blame at Charlie McCreevy's feet for going on with a very bad decision. I would also question the Taoiseach's actions."
The Sinn Fein president, Mr Gerry Adams, welcomed Mr O'Flaherty's decision and said the Government's behaviour during the "whole process has been diabolical".
"This whole sorry mess could have been avoided if the Government had advertised the post in open competition and an independent body had been in place to process public appointments."
Workers' Party spokesman Mr Shay Kelly highlighted Ms Harney's and Mr McCreevy's role in the affair and suggested they should review their positions. "Mary Harney has tonight come out of the ivory tower in which she has been ensconced for weeks as if she were a mere onlooker.
"While it has taken a very long time at least Mr O'Flaherty finally had the common sense to fall on his sword. I don't, however, hold out much hope that Minister McCreevy will do likewise," He said. "Maybe Ms Harney too could consider a ritual sword-falling tonight."