We are almost 40 days waiting on the formation of a coalition
Two groups of Independents have indicated they will abstain in votes for a new Taoiseach on Wednesday.
Their stance means neither Enda Kenny or Micheal Martin will have made any ground in their efforts to form a new government.
Fine Gael and Fianna Fáil are both seeking support for the ballots for Taioiseach.
But both the Independent Alliance - containing six TDs - and the Rural Alliance - of five members - say they will not back either candidate for the time being.
The groups have also hit out at a tweet by acting Health Minister Leo Varadkar, which said his election posters were "cleaned, counted, stored and ready to be deployed" - indicating a second election could be likely.
My posters cleaned, counted, stored and ready to be deployed pic.twitter.com/TPiAU1ZMcM— Leo Varadkar (@campaignforleo) April 3, 2016
TD Shane Ross says they will not negotiate "under threat" that there is a general election looming.
While Dublin Bay North deputy Finian Mc Grath says people want the TDs they elected to get on with government.
Earlier, Kerry TD Michael Healy-Rae said the real talking needs to take place between the two main parties.
"It's time to get on with the programme - I would have rathered if the party leaders had done their jobs over the weekend, but they didn't so we are where we are," he said.
Mr Martin and Mr Kenny were twice in contact via telephone calls and text messages last week, but full talks will not take place until after the next vote for Taoiseach on Wednesday afternoon.
It was reported on Friday that representatives of the Independent Alliance could make a decision Tuesday as to which of the major parties they will give their preference to.
At the time, Independent Alliance member Shane Ross said that there was 'no offer on the table' and that there was 'no government for government in draft' at that stage.
These comments came a day after Mr Kenny stated that Fine Gael were close to a programme for Government with Independents.