Fianna Fáil leader Micheál Martin has said he does not see the current Dáil lasting until April unless he and the Taoiseach can agree the date for a general election.
Mr Martin said he believes "the whole thing will unravel very quickly" in the New Year if the two party leaders do not set a programme to wind it down.
Mr Martin said the Dáil will become "untenable" it there is no such agreement.
"One would be going week-to-week with no programme, you are open to independents having to vie with each other and the whole thing would unravel very quickly," he said.
The motion of no confidence in Minister for Housing Eoghan Murphy showed how independents were trying to second guess each other, he said.
"So my experience tells me that the situation would unravel very quickly if you don't have a clear programme of substance as opposed to short-termism."
Mr Martin wrote to the Taoiseach earlier this week to request such an agreement, but he said Mr Varadkar has not replied and there is now little chance of them meeting before Christmas.
"I think he is weighing up his options at the moment," Mr Martin said.
Mr Martin said his party, through the confidence and supply agreement, has "contributed significantly to the stability of the country" particularly through periods where there was a risk of a no-deal Brexit.
"Overall, in contrast to British politics, many people have commended the fact that Ireland, and the Irish political system, has been able to respond with a good degree of consensus on the big issue for the country in terms of the national interest."
He said his preference after the next election is a Fianna Fáil-led government with other parties, as opposed to another confidence and supply deal.
Asked what smaller parties would support Fianna Fáil if it had the largest share of seats, Mr Martin said: "There is quite a range of smaller parties, you have the Labour Party, the Green Party, the Social Democrats and others. But that is up to them as well, they will have their choices and their views but that is where we see it in terms of the next government.
"Obviously we want to achieve the maximum number of seats that we can and that will enable us to lead the next government."
He said: "Fine Gael has been in power for eight years and they have failed to deliver on key issues, so there is a need for an alternative."
Mr Martin also said he is concerned about interference and misinformation in the forthcoming general election campaign and said the Online Advertising and Social Media (Transparency) Bill, which aims to combat online fake news and online misinformation, must be passed before then.