Negotiations teams to review the deal keeping the Government afloat will be appointed this week.
A poll has found that 44% of people would prefer to have a General Election than try and make the current government work.
The Irish Times/ IPSOS poll out this morning also shows that 46% would prefer an extension on the confidence and supply arrangement.
The poll, which was carried out at the end of last week, also shows Fine Gael remain the most popular party on 33% up two points.
Fianna Fail are down 1% to 25% and Sinn Féin are slightly behind on 24% with a rise of two points.
Taoiseach Leo Varadkar and Fianna Fáil leader Micheál Martin met last night to discuss the confidence and supply deal that keeps the Government in place.
They agreed to appoint negotiating teams this week and in a joint statement said their first meeting will be next week.
Mr Varadkar wants an extension of the confidence and supply deal until 2020.
Mr Martin called for neither of them to collapse the Government until Brexit has been dealt with, with some in his party unwilling to lock in for another two years.
The talks will largely be influenced by what comes out of Brexit negotiations over the next few weeks.
If a deal there remains elusive neither Fine Gael or Fianna Fáil will want to be seen to bring down the government at such a sensitive time, but if a final agreement looks more concrete the Taoiseach may be encouraged to seek a more stable mandate from the people before Christmas.
However, the scramble over the weekend to shore up the support of Independent TDs would suggest that, for now, the threat of an election has receded.