Tánaiste and Minister for Education Mary Coughlan has said she regrets her colleague Jim McDaid's decision.
Dr McDaid resigned as TD for Donegal Donegal North East.
Ms Coughlan said his view that any Government should have a significant majority is not reasonable at the moment.
She said it was not the case, as claimed by Dr McDaid in a letter to Taoiseach Brian Cowen, that the Government is not making tough decisions needed to correct the current economic situation.
She said the Government is focused on the budgetary process.
The Fine Gael leader told the Dáil that the Government lost another man overboard.
Enda Kenny said Dr McDaid advocated a General Election. Mr Kenny said the Taoiseach continued to brazen it out when he no longer has a valid authority.
He said that no-one believed the Government anymore and that the only thing of credibility would be if the Government went to the people.
The Taoiseach said he would expect a better sense of responsibility from the Fine Gael leader.
Speaking during Leaders' Questions, Mr Cowen said the budgetary plans were on track and expenditure is under control.
He said the Government's intention was to do its job and duty, adding that the authority of the Taoiseach was decided by the House.
Mr Cowen wished Dr McDaid well.
Resignation comes into effect
The Ceann Comhairle announced in the Dáil that the resignation of the outgoing TD for Donegal North East has come into effect.
Dr McDaid, a former minister, said 'purely personal reasons' were behind his decision.
In a letter sent to Taoiseach Brian Cowen last week, Dr McDaid criticised the Government for failing to make significant progress on reducing the deficit and said a General Election would be in the best interests of the Government and Fianna Fáil.
Dr McDaid's decision leaves the coalition parties with a majority of three.
Dr McDaid said that while some courageous decisions had been made, after two years the Government had failed to make any significant progress in reducing the structural Budget deficit.
'Our primary focus has been on the survival of Government instead of the health of the economy'.
He added that in the best interests of Ireland, the Government has to have a working majority in the Dail of at least 20 seats.
A Government spokesperson has confirmed that Dr McDaid's letter to the Taoiseach was received last Thursday, and an acknowledgement posted on Friday.
They said a substantive response to the points raised in the letter was to follow in due course, as is normal.
In November 2008, Dr McDaid abstained from a vote on a Fine Gael motion calling for the cervical cancer vaccination programme to go ahead. He automatically lost the party whip then.
Dr McDaid said during the debate that even though these were difficult economic times, the withdrawal of a life-saving vaccine was not a move he could support.
In November last year he withdrew his support for the Government, saying he would consider voting against it 'if and when necessary'.
Government sources said they were not relying on Dr McDaid's vote in the Dáil and are confident of retaining a majority in the House.
State of the parties
With four vacant seats - due to resignations of George Lee, Martin Cullen and Dr McDaid, and the election of Pat the Cope Gallagher to the European Parliament - there are 162 sitting TDs.
The Ceann Comhairle does not vote unless there is a tie, which means 81 votes is a majority.
At present, there are 70 TDs in the Fianna Fáil parliamentary party, six Greens, and three Independents - Mary Harney, Michael Lowry and Jackie Healy Rae - committed to supporting the Government.
In addition, there are three TDs outside the Fianna Fáil parliamentary party who usually vote with the Government - Mattie McGrath, Jimmy Devins and Eamon Scanlon.
On the other side are 51 Fine Gael, 20 Labour, and four Sinn Féin TDs, giving 75 votes firmly committed against the Government.
There are four Independents who tend to, although not always, vote against the Government - Joe Behan, Noel Grealish, Finian McGrath and Maureen O'Sullivan.