There is a call by members of the Oireachtas Committee on the Eighth Amendment for a referendum on abortion to be held next May.
The committee has already said it will publish its report on the matter by the end of the year.
People Before Profit TD Brid Smith says she is in favour of an early referendum to repeal the Eighth Amendment of the Constitution.
She said: "We need an early referendum, it has to be in May because it has been young people driving the demand for access to abortion and they will be around in May.
"They won't be necessarily around in June or July, they are already signing up now to be registered to be able to vote, and we have to give them that access."
However, Fine Gael TD Peter Fitzpatrick is against repeal and says women in the UK are having abortions in the case of Down Syndrome.
He said: "I want to record my shock and sadness at the fact that 125 babies lost their lives because they were diagnosed with this condition.
"There is no doubt that babies with Down Syndrome are at increased risk if we repeal the Eighth Amendment."