An Independent Alliance TD says he does not think a new Taoiseach and Government will be appointed on Wednesday.
Fine Gael is due to meet with the alliance on Monday, in a bid to secure the group's support for a minority government.
A draft deal was put together by negotiation teams from Fine Gael and Fianna Fáil yesterday evening, which has yet to be approved by the parties' TDs.
Independent Alliance TD for Longford Westmeath, Kevin 'Boxer' Moran, says he and his colleagues still have a lot of issues to work through with Fine Gael.
He said: "I don't think we'll have a government on Wednesday, I know a lot of people are saying we will, I believe it'll be Thursday it could even go to Friday.
"We ourselves are only halfway through our talks in our final document with Fine Gael, it's 132 pages and we have a fair bit of that to go through yet.
"But we will rush the talks, we won't be doing what was going on last week, going in for two hours and out. If it means going in until 12 o'clock or until two in the morning, we have no problem doing that."
Meanwhile, Sinn Féin TD Sean Crowe thinks it was not a good idea for Fianna Fáil to do a deal which allows Fine Gael potentially form a new minority Government.
He thinks Fianna Fáil will be punished by voters in the next election.
He said: "They ran the election on the basis that they were going to oppose Fine Gael and Enda Kenny and they've done a complete u-turn on that.
"I think they've lost any credibility in relation to the position of the leader of the opposition, the two conservative parties have come together. It's not going to be a good thing for working people and their families.
Mr Crowe said he doubts that the government will last any length of time.
He said: "When people do get the opportunity, I think those larger parties are going to suffer for that, in particular Fianna Fáil."