Irish finance minister Brian Lenihan is due to enter talks with opposition parties over the fast-tracking of legislation that will give effect to the budget and bring forward a general election in Ireland.
The Irish Government was left on the brink of collapse after the junior coalition Green Party pulled the plug, blaming a complete breakdown in trust and patience in partners Fianna Fail.
The Greens have vowed to support the Finance Bill from the opposition benches and claimed Fine Gael and Labour agreed to ease the passage of the legislation.
Labour has threatened to press ahead with its motion of no confidence in the government unless the bill is rushed through by Friday and the Dail dissolved - meaning voters could go to the polls next month instead of March 11.
But Mr Cowen and Mr Lenihan have warned the timeframe is unrealistic.
The Taoiseach said: "The important thing now is to have an orderly completion of the Finance Bill in the interests of the country and then obviously we move to a dissolution of the Dail and a general election."
Talks will begin between Department of Finance officials and the opposition finance spokesmen to discuss a timetable for the passage of the legislation through parliament. Sinn Fein opposes any pact between parties to get the bill through before an election, with Independents Michael Lowry and Jackie Healy Rae are due to declare their stance later.
Meanwhile, Mr Cowen has said has no intention of resigning as Taoiseach and dissolving the government, instead reassigning the Cabinet positions of Green Party leader John Gormley and communications minister Eamon Ryan. With six other resignations from Cabinet in the last week, and the Greens stopping them from being filled with new faces, the majority of government ministers are already double-jobbing or two triple-jobbing.
As his party left government, Mr Gormley said the Irish people had begun to lose confidence in politics and deserved better. "For a very long time we in the Green Party have stood back in the hope that Fianna Fail could resolve persistent doubts about their party leadership," he said.
"A definitive resolution of this has not yet been possible. And our patience has reached an end. Because of these continuing doubts, the lack of communication and the breakdown in trust, we have decided that we can no longer continue in government."