A new group within the TUI is calling for the teachers' union to take a tougher stance with the Government
The former Tánaiste has warned that people have to be able to live on a week's wages.
Labour's Joan Burton wants the Taoiseach to start talks on increases for public sector pay.
The Lansdowne Road Agreement - the latest deal designed to continue restoring salaries, following the previous Haddington Road Agreement - has only been in force for around four months.
However, recent weeks have seen increasing demands - from both unions and opposition parties - for an early start to the next round of negotiations over public sector pay.
Deputy Burton explained where she thinks the extra money could come from.
Speaking to Newstalk Breakfast, she explained: "[We should] actually have an economy that functions and does well by fairness - so that when people get a week's wages they're actually able to live on that.
"[It's] not doing what was done during the Celtic Tiger, [when] some sections took far more of their slice of the cake than anybody else," she argued.
Meanwhile, a new group within the TUI is calling for the teachers' union to take a tougher stance with the Government over pay.
The newly formed "Grassroots TUI" group wants the union to pull out of the Lansdowne Road Agreement.
It is also seeking the reform of the TUI.
An increasing number of public sector unions have been calling for fresh negotiations with the government in the wake of the deal reached with Garda associations earlier this month.
Ministers have insisted that the deal - which members of the GRA and AGSI are being balloted on - is within the Lansdowne Road Agreement.
Yesterday, the Irish Congress of Trade Unions (ICTU) said it will advise its affiliated unions in the private sector to seek pay increases of 4% next year.
John Douglas, Chair of ICTU's Private Sector Committee, argued: “People have seen their living standards either stagnate or fall over recent years as a result of austerity and rising costs. The best way to address this deficit and to help grow the economy is through wage increases."