A number of Ministers have also expressed doubt that the public will support legislation giving effect to the recommendations of the Oireachtas Committee on the Eighth Amendment.
The Cabinet will consider changes to Ireland's abortion laws this morning.
As well as recommending that the effective ban on abortion be removed from the Constitution, the committee recommended that a lawful termination be available without restriction up to 12 weeks of pregnancy.
"As far as my party is concerned, the Fine Gael party, I want us always to be a warm house and a big tent for people with a diversity of views on this issue whether pro-life, pro-choice or in that very big grey area in between".
Minister for Social Protection Regina Doherty was understood to have expressed similar reservations. Some others Ministers were non-commital.
Both Mr Kehoe and Minister for Business Heather Humphreys said they had been lobbied heavily by Fine Gael members on the issue.
While Varadkar has said that his Cabinet would take a collective decision on whether to hold a referendum, he has said that ministers would be able to "dissent" from that.
Mr Varadkar said there were diverse views at cabinet during a discussion about the likely referendum on the Eighth Amendment. The Government wants to hold the referendum either in May or early June.
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Leo Varadkar says the Oireachtas committee's recommendation of abortion on request up to 12 weeks, went further than he expected.
"There is a concern understandably among many politicians that perhaps for the majority of the public that proposal might go one step too far".
The eighth amendment of the Irish constitution, introduced in 1983, gives an equal right to life to a pregnant woman and an unborn child.
Health Minister Simon Harris will present his plans for a referendum and the new laws that could come in.
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Because you know we're moving they make you... "Kinda getting there", she said inspecting her grill in her phone's reflection. And while we've seen mention of a "Meaning of Life World Tour", we're still awaiting dates to be announced for that run.
Labour leader Brendan Howlin urged Mr Varadkar to bring the proposal to hold a referendum to the Dáil as soon as possible.
"I believe it is important now in the context given in the partnership programme for government that we move on towards the next stage".
Speaking today, Minister for Justice Charlie Flanagan said the issue has been a "challenging and sensitive" one but that he supports the recommendations of the committee.
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