Taoiseach Enda Kenny has asked three of his most high-profile and liberal ministers to "convince the rest" that legislation is the right move.
The three ministers are to hold a series of meeting with conservative ministers and backbench TDs in an effort to "bring the party together" in the wake of the tragic death of Savita Halappanavar.
"It's no mean task," said a source.
"At least two dozen TDs are against what is recommended in the report of the expert group on abortion.
"The plan announced yesterday gives a very short time space for people to fall into line. Fine Gael really doesn't want this to descend into an internal fight."
The source added: "Let's be honest, there is never going to be a consensus on this issue but if we can keep the public bickering to a minimum then that will be an achievement."
Justice Minister Alan Shatter made a strongly worded speech last night in he which he outlined his belief that "modern language" was needed to replace the State's 150-year-old abortion laws.
"Whatever action Government takes, we will still have in this country one of the most restrictive laws in Europe with regard to the termination of pregnancies," he said.
He noted that while new legislation would eventually deal with the fallout from the 1992 X Case, it would not go so far as to address other issues such as the termination of a pregnancy resulting from rape, or where there is a foetal abnormality.
"In the absence of constitutional change there will continue to be a British solution to this Irish problem," he said.
"We should also be clear on what we are not doing. We are not considering, in any shape or form, abortion on demand as is alleged by some."
However, several TDs have voiced serious concerns about the speed at which the Government is progressing with its response to the expert group's report.
The Cabinet has decided to debate the report in the Dail next week and will make a decision on what to do next before Christmas.
The Oireachtas health committee will convene in January to discuss the report and it is expect that legislation will be drafted early next year.
The Taoiseach said the Government would address the suicide grounds in its response and that it would not just be "a box-ticking exercise".
He is now on a direction collision course with many backbenchers and even some ministers.
Last night European Affairs Minister Lucinda Creighton noted that 95pc of abortions carried out in the UK in 2009 were on mental health grounds.
She argues that pushing through a decision before Christmas will limit the opportunities for debate.
Ms Creighton also pointed to Fine Gael's pre-election promise not to introduce legislation.
At a party meeting Mr Kenny's constituency colleague John O'Mahony warned other TDs not to take his support on the issue "for granted".
Others, including Terence Flanagan, Billy Timmins and James Bannon, also raised concerns last night.