Children's Minister Frances Fitzgerald warned that rebel backbenchers will lose the party whip and their position in the parliamentary party.
She said that while Taoiseach Enda Kenny does not want to lose any deputies, he has “nailed his colours to the mast” regarding the “important legislation”.
“I want to emphasise this, we are talking about a woman’s life, where a woman’s life is at risk,” Ms Fitzgerald added.
“We are talking about a very strict, precise, focused piece of legislation.”
TDs have passed the second stage of the Protection of Life During Pregnancy Bill earlier this evening, by 138 votes to 24.
Four Fine Gael TDs voted against - Peter Mathews, Billy Timmins, Brian Walsh and Terence Flanagan.
The so-called "suicide clause" has been the biggest bone of contention among Government TDs.
Ms Creighton and a further half dozen members of the party may yet refuse to support the legislation if it is not removed.
They have argued suicide should not serve as legal grounds for the procedure, with some claiming a termination could do more damage to a woman’s mental health.
Meanwhile, Sinn Féin TD Peadar Toibin also faces expulsion from his party for voting against the legislation.
Other TDs to reject it include 13 from Fianna Fáil.
The Government, which hopes to have the new laws enacted by the end of July, has faced much criticism throughout the emotionally-charged and divisive debate.
Around 20,000 pro-life campaigners took to the streets in protest against the legislation last month, arguing the limited laws would lead to widespread demand for terminations.
The Taoiseach also revealed he had been sent letters written in blood and plastic foetuses for his decision to press ahead with the legislation.
An estimated 4,000 Irish women travel to the UK every year seeking an abortion.
The Government was forced into action and committed to legislating for the procedure in limited circumstances after the death of Indian dentist Savita Halappanavar who suffered a miscarriage and subsequently died in hospital in Galway.
If enacted, the Bill will legalise abortion where there is a real and substantial risk to the life of the mother, including the threat of suicide.
It aims to legislate for the X case judgment from Ireland’s Supreme Court, which found abortion is legal if there is a real and substantial risk.
The case was taken by a 14-year-old rape victim who became pregnant and was refused permission to travel for an abortion.
The European Court of Human Rights also previously found that Ireland discriminated against a woman in remission with cancer who was forced to travel overseas for a termination.