Fianna Fáil has pulled out of the contest to form a minority government but differences over Irish Water could scupper the chances of a Fine Gael-led minority government getting off the ground.
If the two parties cannot reach agreement on water and the rules to enable a minority government to function, another general election in May becomes a real possibility.
In the coming days Fine Gael will attempt to assemble the numbers to have Enda Kenny elected taoiseach at the fourth attempt next Wednesday, following yet another unsuccessful series of votes yesterday.
As well as talking to Independents in the coming days, Fine Gael will seek to persuade the Labour Party and the Greens to vote for Mr Kenny and participate in a minority government.
However, these groupings will be influenced by the progress of talks between Fine Gael and Fianna Fáil about how the operation of a minority government can be facilitated.
The attempt by Micheál Martin to force the hand of the Independents yesterday backfired when 14 of them came together and agreed to abstain on the Dáil vote for taoiseach.
His nomination was defeated by 91 votes to 43, a margin of 48. While Mr Kenny was also defeated, the margin was considerably smaller at 25.
Dublin South-West Independent Katherine Zappone voted for Mr Kenny as did Tipperary TD Michael Lowry and all 50 Fine Gael TDs to bring the total in favour of his nomination to 52 with 77 voting against.
Fianna Fáil indicated late yesterday that Fine Gael must prove it has the declared support of at least an additional six TDs before Mr Martin agrees to facilitate the election of Mr Kenny as taoiseach next week.
Mr Martin told a meeting of his parliamentary party that during negotiations with Fianna Fáil, Fine Gael had insisted it had the support of an additional six or seven deputies.
He said Fine Gael must prove it has the support of those TDs locked down before the next vote on candidates for taoiseach takes place.
Mr Kenny must secure the support of 58 TDs if he is to be elected taoiseach in a scenario in which Fianna Fáil abstains.
Mr Martin told Fianna Fáil TDs Mr Kenny’s cabinet must include Independent members in order to secure Fianna Fáil support.
Tánaiste Joan Burton is understood to be actively encouraging the Labour Party to re-enter government. Ms Burton has been seeking support for her proposal from TDs and Senators.
A party source confirmed the seven TDs may be willing to support Mr Kenny’s nomination as taoiseach if progress has been made.
However, a Fianna Fáil source said it would not support a minority Fine Gael government if Labour was in coalition with them.
“Why would we support the re-election of the previous government when we fought the election to remove them from government? We just would not do it.”