The Independent Alliance has said it will make a decision on Tuesday on whether or not it will back Enda Kenny or Micheal Martin for Taoiseach.
The Dail will vote again on Wednesday - however neither of the men is expected to receive enough votes.
Talks aimed at forming a coalition are due to resume on Monday after taking a break this weekend.
Last night the Taoiseach said he believed they were close to a programme for Government with independents.
However the Independent Alliance's Shane Ross has said both Fianna Fail and Fine Gael need to show a sense of urgency: “There’s no offer on the table at the moment, there is no final document.
“There is no program for Government in draft at this stage.
“What we have done is gone through all the topics, gone through them in an enormous amount of detail, but we haven’t thrashed out an agreement of any sort.
“It would be much more helpful if they were to get together and show a real sense of urgency about it.”