Update - 6.45pm: The acting Justice Minister has said it is "unlikely" there will be a vote to elect a new Taoiseach this week.
Frances Fitzgerald's comments came as Fine Gael continued its talks with Fianna Fáil on forming a minority government.
Earlier: Independent TD Danny Healy-Rae says neither he or his brother Michael will vote for Enda Kenny as Taoiseach if there is a vote on the issue in the Dáil tomorrow.
Fianna Fáil and Fine Gael are back around the talks table this afternoon, with the contentious issue of Irish Water set to be the biggest stumbling block.
He told Radio Kerry he was very hurt by the actions of both parties in attacking independents in the media last weekend.
Mr Healy-Rae said: "Some people say we are supposed to be the meat in the sandwich, I say we are not even the butter.
"When I see what's going on and that Fianna Fáil are prepared to vote to support Fine Gael, it makes no difference to me what Fianna Fáil say, they are supporting a Fine Gael government - whether it is minority or otherwise - they have the vote between the two of them not to need any independents."
One of the Fianna Fáil negotiators says with goodwill and compromise they can conclude a deal to facilitate a Fine Gael minority government.
Fianna Fáil's Barry Cowen was giving little away on Irish Water.
He said: "Look, it is like many other issues that are contained in our manifesto."
His colleague Michael McGrath said there was good progress, but that nothing was agreed until everything is agreed.
He said there were no deadlines, but also said: "There are some thorny issues yet to be agreed, that does require goodwill on all sides and indeed compromise."
And that compromise is being signaled from Fine Gael's Simon Coveney, who said: "Obviously the parties have had differences on a number of issues and we are trying to work our way through those differences to find compromise and a way forward."
But Irish Water is the biggest stumbling block and senior Fine Gael sources say it is being left to them to "fix it".
However, there is an increasing sense that a deal could now be hammered out to allow for the election of Enda Kenny as Taoiseach on Thursday.