Fianna Fáil was growing in its belief that it can take two seats in Ireland South as ballots began to be piled on Monday.
The party's sitting MEP Billy Kelleher was set to be elected on an early count, but party operatives said they were "pleasantly surprised" by the vote amassed by former RTÉ journalist Cynthia Ní Mhurchú.
The Carlow woman looked set to have the fourth-most first preferences and would likely benefit from the surpluses of Seán Kelly — who became Ireland's first MEP in this election when he exceeded the quota on the first count on Monday evening — and Mr Kelleher when he is elected.
Ms Ní Mhurchú was set to trail independent Clare TD Michael McNamara but will find herself ahead of independent MEP Mick Wallace, Green Party MEP Grace O'Sullivan, and Fine Gael's John Mullins.
The shape of the ballots, however, meant that Sinn Féin was in a fight to take a seat.
Its leading candidate Kathleen Funchion was in sixth place and will hope that transfers from the party's other candidate, Senator Paul Gavan would be enough for her to close the gap on Mr Wallace and Ms Ní Mhurchú.
Fianna Fáil sources said that they were "delighted" to be in with a chance at a second seat, while Fine Gael figures said that they had hoped Mr Mullins would have a chance for the seat, but that it had been "difficult" to convince people in Cork to vote for him ahead of Mr Kelly.
One source said that Mr Kelly "has an appeal beyond Fine Gael, which is a good thing and a bad thing".
There had been hope that the count in Nemo would take place in the morning, but the size of the vote meant that this timeline was delayed. It is now expected that the count will continue on until Thursday at the earliest.
"It's not the day that we wanted to have, it's important to be honest about that."
Ms Funchion said that Sinn Féin would have to "regroup" after the results and "see where it didn't work out", despite an overall increase in the number of local authority seats the party holds.
"It's really important that we are match fit for the general election because I think we need a change of government.
Mr Kelleher said that he believes the next European Parliament will contain a majority from the groupings which Fine Gael (EPP), Fianna Fáil (Renew), and Labour (S&D) belong to, which will head off the surge of far-right parties in Europe.
However, Mr Kelleher said that he would not vote for Ursula von der Leyen to retain her position as European Commission president.
"It's an interesting election because there was a debate around the whole issue of the extremes on both left and right, where the centre would reside in modern Irish politics.
"And I think that was answered emphatically yesterday, both in the local elections but also in the European elections where people looked at the alternatives and wanted to go back to the centre, to stability, making sure that there was some politics, decent politics, and politics that was proactive in terms of engaging with Europe.
"With regard to Ursula von der Leyen, I have been very clear throughout this election.
"I stated in advance of the election, I said during the election, and I'm saying after the election that I will not be supporting the nomination of Ursula von der Leyen."
Meanwhile, Mr Kelly said that a "pot of EU money" could and should be used to regenerate Irish towns and villages and better support struggling SMEs.
Seeing struggling businesses and towns battling dereliction while he was out on the campaign trail was hugely concerning, Mr Kelly said.
“SMEs are a neglected sector. Most of them are family-owned businesses.
“It did grieve me, going from town to town, to see many smaller, beautiful shops genuinely struggling.
"Some are barely able to make ends meet because rates have increased, cost of living, the minimum wage has gone up, they’ve all hit them together. We need to do something about it.”
Ireland should tap into funding at the EU level to tackle this creeping decay, he said.
InvestEU, a European Investment Bank initiative could be used to help struggling communities in Ireland, he said.