Independent TD Michael Lowry, who supports the Government, says he would not be willing to back another Fianna Fáil nominee as Taoiseach if Brian Cowen were replaced.
The Tipperary TD is also demanding a summit of Government and Opposition leaders to discuss the state of the economy.
In a statement, Mr Lowry insisted that the leadership of Fianna Fáil is a matter for that party.
However, in a clear warning about his support for the Government, he said that he would not support another Fianna Fáil nominee without a General Election.
He went on to call for a meeting of the Taoiseach and Finance Minister Brian Lenihan with Opposition leaders and spokespersons.
This conference, he says, should share a full, frank, open and honest outline of the state of the economy by the Department of Finance.