People Before Profit have called for the minimum wage to be raised to €15 per hour with people now experiencing a “cost of survival crisis”.
The party has urged workers to put in “significant pay claims” that at least match the current rate of inflation.
Meanwhile, the Government has said it will finalise a package of measures to tackle the cost of living “very shortly”.
People Before Profit tabled a motion to increase the minimum wage in the Dáil on Wednesday, which the Government did not oppose.
However, Dún Laoghaire TD Richard Boyd Barrett said while the Government would accept the motion, they had "absolutely no intention of actually acting on it".
“The public should know that this is the cynical way in which politics operates in here and the way this Government behaves,” he said.
“They [the Government] are spineless but behind the scenes they operate to maintain the status quo and effectively ignore the really desperate situation that working people are facing at the moment as a result of the Government’s own failures.”
Mr Boyd Barrett said Fianna Fáil junior minister Sean Fleming's remarks that people should look to switch their utility providers and where they shop rather than "complaining" about what the Government was doing was "not some Maverick comment" but instead "the Government's policy".
"It has been the Government's policy and Fianna Fáil and Fine Gael's policy for 20 years since you removed the not for profit mandate of the ESB, privatised Bord Gáis - energy prices have gone through the roof and now we are really paying the bitter price for that."
Solidarity TD Mick Barry said while the minimum wage had increased by 2.9 per cent at the beginning of the year to €10.50 per hour, inflation stood at 5.5 per cent and asked how people were supposed to survive on this "in the current climate".
“As was put to me at the weekend, this is now not a cost of living crisis, it is a cost of survival crisis,” he said.
Mr Barry said minimum wage workers were not a “tiny minority” and are nearly 10 per cent of the workforce and that 50 per cent of minimum wage workers have attended third-level education .
People Before Profit TD Paul Murphy said the minimum wage in Ireland was "a poverty wage" with a full-time minimum wage worker earning €21,000 per year.
He said the HSE chief executive Paul Reid was earning 20 times the wage of a minimum wage cleaner and the Taoiseach earning 10 times that which was "simply not right".
“We need to raise the wages for the low paid and cut them for the tiny few at the very top,” he said.
The Dublin South-West TD said while TDs and senior officials had gotten “pay rise after pay rise” low paid workers were expected to “make do with less”.
Sinn Féin TD Louise O’Reilly said people will be “shopping around for a new Government” as they “cannot take much more of this”.
Independent TD Thomas Pringle said "shopping around" ignored people in rural Ireland and that some of his constituents in Donegal might only have one local shop.
The Minister of State with responsibility for Law Reform James Browne said Government ministers and their officials have been tasked with developing proposals for a package to help families with the cost of living, with the package due to be finalised "very shortly".
He said the minimum wage had increased from €8.65 to €10.50 between 2016 and 2022 in line with proposals from the Low Pay Commission and that it was due to make recommendations at the end of July.