During a lifetime of hearing it played and cited too many times, Mary Lou McDonald has come to loathe the Ricky Nelson song Hello Mary Lou and its cheery declaration of love for the girl who flashes “big brown eyes”.

Hello, Mary Lou,

Goodbye heart.

Sweet Mary Lou,

I’m so in love with you

The Sinn Féin leader had better brace herself, because after Ireland’s general election on Saturday, the media and her party colleagues may well barrack her with the lyrics, channelling them into headlines and belting them out at rallies.

Much of Ireland, after all, has indeed fallen for her. An opinion poll this week showed her approval ratings soaring and Sinn Féin becoming the Irish Republic’s most popular party.

Commentators are calling it historic, a breakthrough for the republican movement that could realign Irish politics after a century of domination by two centrist parties, Fianna Fáil and Fine Gael.

The IRA slogan “tiocfaidh ár lá” means “our day will come”, but not even Sinn Féin – the terrorism group’s political wing during the Troubles – anticipated the surge. It has captured a mood for change and wrongfooted Leo Varadkar, the taoiseach and Fine Gael leader, and Micheál Martin, the leader of Fianna Fáil.

At the core stands McDonald, 50, the personable Dubliner who succeeded Gerry Adams and may turn Sinn Féin into a party of government. As one wag put it in a letter to the Irish Times: “Have Leo and Micheál met their Mary Lou?”

In Cabra, a working-class area of McDonald’s Dublin Central constituency, many root for her to shake up what they consider an an ossified party duopoly past its expiry date.

She’s better than any of the men. She really fights. I love the way she talks to people Ann Smith

“She’s better than any of the men,” said Ann Smith, 75, a grandmother out walking her dog. “She really fights. I love the way she talks to people, especially the men. She’s well able for them.”

For a movement that dates from the 1916 Easter Rising it is quite an arc: a succession of leaders with a whiff of sulphur culminating in a mother-of-two who studied English literature at Trinity College Dublin.

“She’s very bright, articulate, self-confident and a good debater,” said Deaglán de Bréadún, the author of Power Play: The Rise of Modern Sinn Féin. “I’d say Sinn Féin couldn’t believe their luck when she joined. She’s such a good performer on radio and TV and it’s probably a help with southern voters that she doesn’t have a northern accent. All in all, it’s very hard for her political opponents to pick holes in her image.”

Talk of seismic breakthrough may be overdone. McDonald is not about to become taoiseach. Sinn Féin’s results traditionally underperform opinion polls. The party fielded just 42 candidates for the 160-seat Dáil Éireann, the lower house of the Irish parliament, so will not fully translate support into seats.

Analysts expect Fianna Fáil to win about 50 to 55 seats, Fine Gael perhaps 35, and Sinn Féin 26 or at most 30. The two establishment parties have ruled out forming a coalition government with Sinn Féin, but it may yet play kingmaker.

“It’s not revolution, it’s evolution,” said Dr Theresa Reidy, a political scientist and election expert at University College Cork. “For Sinn Fein it’s more about consolidation.”

Even so, McDonald finds herself leading a remarkable turnaround. A party Irish voters used to shun as radioactive, an off-putting mix of Northern Ireland accents and Troubles vibes, has overtaken leftwing rivals and established itself as a voice for those who view Fianna Fáil and Fine Gael as the Tweedledum/Tweedledee stasis.

McDonald grew up in Rathgar, a middle-class suburb of Dublin, and attended a Catholic school, Notre Dame des Missions, before studying Sylvia Plath and metaphysical poets at Trinity, formerly a Protestant bastion.

She worked as a researcher at the Institute of International and European Affairs, a thinktank, before joining Fianna Fáil, the party of her parents, before switching to Sinn Féin in 1999, a year after the Good Friday agreement.

One version says she left because a Fianna Fáil bigwig stymied her advancement. McDonald’s version is she wanted a better fit for her principles about social justice and Irish unity.

She’s very bright, articulate, self-confident, a good debater. Sinn Féin couldn’t believe their luck when she joined Deaglán de Bréadún

“She’s not lacking in political ambition but has fully converted to Sinn Féin ideology. You don’t thrive in that party without buying into its Irish republican mindset,” said De Bréadún.

The party fast-tracked McDonald up the ranks: an MEP in 2004, a TD (MP) in 2011, then succeeding Adams as party leader in 2018. She praised him as her “political mentor” and ended a speech with “tiocfaidh ár lá”.

McDonald can be “wooly” on detail but speaks with a passion that distinguishes Sinn Féin from other parties, said Reidy, the professor.

Voters at first seemed unmoved. They abandoned Sinn Féin in a 2018 presidential election and in 2019 council and European parliamentary elections. The party braced for more losses in the general election, so fielded few candidates. Then the poll numbers started rising – and rising.

The economy hums at near full-employment but voters are fatigued with the Fine Gael-led government, which was propped up by Fianna Fáil, and angry at hospital bed shortages and soaring rents. McDonald, ably supported by party colleagues Pearse Doherty and Eoin Ó Broin, has cast Sinn Féin as a vehicle for change.

The party keenest on unification paradoxically benefitted from voter indifference towards Northern Ireland. Barely a blip in the campaign, it let Sinn Féin focus on bread-and-butter issues.

That changed this week when a notorious 2007 murder returned to haunt the party, forcing McDonald to revisit Sinn Féin’s links with the IRA since the Troubles.

Some voters recoiled. “Too many unanswered questions,” said Michelle Walsh, 51, a Dublin Central constituent who does not plan to vote for McDonald.

Claire Beatty, 45, another constituent, said history had “leaked” out but that McDonald’s party still represented change. “The past has stuck with them but people are being left with no alternative.”