As a result of the fact their youngest child has reached the age of seven, these families are no longer entitled to claim the payment and will instead be moved to alternative payments.
The change, which has been slammed by a number of organisations representing lone parent families, was introduced during the 2013 Budget and due to be brought into effect in July of this year.
Defending the controversial move, an Taoiseach, Enda Kenny, recently suggested the cuts will be an incentive for single parents to find work, saying: "We cannot allow a situation in an economy that is recovering like ours to bypass thousands of families that are locked into jobless households. That has been one of the real difficulties for so many families."
Justifying the cut which has spent much time in the headlines, he went on to say: "Those jobless households with children are at a particular risk of perpetuating a cycle of poverty that goes on from generation to generation."
Protesting the Government's decision, spokesperson for group, Single Parents Acting for the Rights of Kids, Louise Bayliss, recently said: "A woman I know personally will be down €76 a week in July when these cuts come through. She has a 15-year-old son and already works 20 hours a week."
Explaining the implications the cuts will have on this particular parent, Louise elaborated, saying: "She lives in a deprived area. She has a choice to make - either accept the €76 reduction in her income and face poverty, or work the longer hours and leave her child unsupervised, roaming the streets in a deprived area."
Stuart Duffin, spokesperson for One Family, today said that the move to replace the payment with the Job Seekers Transitional Payment will not be sufficient to bridge the gap between the two benefits, insisting: "Many lone parents are working but they're working 15 to 16 hours a week, which means they do not have access to Family Income Supplement."
Arguing his point on Morning Ireland today, he went on to say: "In addition to that when they were on the One-Parent Family Payment they had an income disregard of €90 a week - the amount of money they could earn before it impacted on their benefit - that is going to be slashed by 30%."
It is understood that Joan Burton was to meet members of the Labour parliamentary party today to discuss changes to the payment
