Sinn Fein, the former political wing of the Irish Republican Army (IRA), had put forward too few candidates to capitalise on a surge of support attracted during the campaign.
The surge of support took Sinn Fein by surprise after it sank to 9 percent in local elections a year ago.
While Sinn Fein is a major force in Northern Ireland, the United Kingdom region where it is part of the power-sharing government that helped end decades of sectarian violence, it has always been a minor player south of the border in the Irish Republic. Fine Gael and Fianna Fail, which are nearly ideologically identical, have largely dominated government since the foundation of the state in the 1920s.
While both Fianna Fail and Fine Gael insist they will not govern with Sinn Fein, citing its IRA past and differing economic polices, such an outcome would demonstrate an appetite for change in decades-long centrist Ireland.
The ruling Fine Gael party is poised for heavy losses.
If the unprecedented results of the exit poll are realised on Sunday following the counting of the votes, it will represent a breakthrough for Sinn Fein challenging the 90-year duopoly of the state's two main parties.
"I do think there is need to change", said Noleen Kelly, 50, who works in the public sector, outside a Dublin polling station.
"I'm lucky enough to have my own place but I look around and I see people struggling".
No party was expected to win enough seats to lead a government by themselves, but various theoretical coalition options have been speculated on in recent weeks, including a FF/SF government or a FF coalition with the Greens and/or Independents, with FF leader Micheal Martin as Taoiseach (prime minister).
Traditionally, islanders vote ahead of the rest of the country to ensure that bad weather doesn't hamper the return of ballot boxes to the mainland in time for the count. Sinn Fein offers a more radical plan to raise taxes on the wealthy, freeze rents, build tens of thousands of new homes and lower the state pension age.
The focus on domestic issues overshadowed Varadkar's greatest success: protecting Irish interests during negotiations over Britain's departure from the European Union.
He said: "Remember, Paul Quinn was beaten to death by a gang of men who broke every single bone in his body".
Mr Varadkar said: "It is odd to meet people who are going to vote for Sinn Fein because they want lower taxes".
But the odds would still be stacked against their current party leader, Mary Lou McDonald, in leading the next government as Taoiseach.
Sinn Fein has made a referendum on Irish unity within the next five years a pre-condition for entering government.
Fianna Fail and Fine Gael, which are closer ideologically, have flatly ruled out any partnership with Sinn Fein.
The Republic of Ireland began voting in a general election, with Prime Minister Leo Varadkar hoping to secure a new mandate on the back of Brexit, but voters are likely to judge him more by his national record.
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