The long period of uncertainty since the Irish general election of February 26th may come to an end when Dáil Éireann, the main house of parliament, meets again this coming Wednesday.

Today the members of the Dáil voted inconclusively for the third time on the nomination of a Taoiseach. But there were indications that, the next time the House sits, Fine Gael leader and head of the outgoing government Enda Kenny may finally come through as the winner.

In today's Dáil sitting, 52 TDs voted for Kenny with 77 against, whereas Fianna Fáil leader Micheál Martin got 43 votes with 91 against.

Talks are now expected to resume between Fine Gael and Fianna Fáil on the formation of a minority government in which one party would take office with the consent of the other party from the opposition benches

There is little doubt at this stage that such a minority administration will be headed by Fine Gael, provided they can secure agreement from Fianna Fáil to refrain from voting against Kenny for Taoiseach in the Dáil.

Otherwise, Kenny will have to request President Michael D. Higgins to exercise his constitutional power to dissolve the Dáil so that another general election can be held. This is an outcome that most members of the Dáil and their parties are very anxious to avoid.

In the previous Dáil vote on the position of Taoiseach, Kenny was supported Fine Gael's 50 Dáil deputies plus Independent TD from Tipperary, Michael Lowry.

There was some surprise this time around when Kenny also secured the support of Katherine Zappone, the newly-elected Independent TD for Dublin South-West. She had stated on Twitter earlier in the day that she intended to abstain.

Born in Washington State, Zappone holds a Ph.D. from Boston College. After the previous general election in 2011, she was appointed by Kenny as a member of Seanad Éireann, upper house of the Irish parliament, on the recommendation of then-Labour Party leader Eamon Gilmore.

There is speculation that, following her support for Kenny in today's vote when most other Independents failed to do so, Deputy Zappone may become a junior minister when a minority government takes office. She is a longtime campaigner for the right to same-sex marriage and the first openly lesbian member of the Dáil.

There is speculation also that the Labour Party may secure a number of ministerial posts in a Fine Gael-led minority government although this might cause problems with the Labour grassroots membership.

Labour was the junior partner in the outgoing government and lost 26 Dáil seats in the general election, reducing its representation to seven TDs.

But in a potentially-significant speech to the Dáil today, Labour Party leader Joan Burton listed a number of items which she said ought to be included in the program for the next government.

These included measures to address the housing shortage, eradicate child poverty, increase the minimum wage, reduce carbon emissions and repeal the constitutional restriction on abortion.

Prior to today's Dáil sitting, Fianna Fáil sources were quoted as saying that it would be the last opportunity for Independent TDs to vote for Micheál Martin as Taoiseach. This was interpreted as issuing an ultimatum to the Independents who have mostly been hedging their bets since the general election.

In the event, none of them backed Martin in today's vote and the way now looks clear for an agreement by Fianna Fáil to stand back and allow a Fine Gael-led administration to take office.

The details of any agreement between the two parties will be closely scrutinized with a view to assessing how long the minority government is likely to last. Fine Gael will be seeking a long-term arrangement but many observers believe another general election will take place within a year or so.

Fianna Fail leader Michael Martin speaks to the press outside Leinster House.Photocall Ireland