However, there are dissenters who will likely make their views clear in the coming days.
The Taoiseach has expressed his hope that a referendum will be held in May, but that timeline means quick movement on the issue will be needed when the Dáil returns next week.
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According to Independent.ie, the Taoiseach said that this question "went further than many people would have anticipated". Following the meeting, Varadkar said that "it certainly went further than I would have anticipated a year or two ago".
The cabinet will make a decision before the end of the month on this issue and Mr Varadkar said it was the Irish government's intention to hold a referendum by the summer. Health minister Simon Harris has suggested that the date could be May 25 if there are no delays in the Dail.
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CVS confirmed to Channel 3 that the company has "no plans to relocate Aetna's operations from Hartford". CVS' chief executive Larry Merlo met with Hartford Mayor Luke Bronin at city hall Thursday.
Some ministers have publicly stated their position while others have not.
"I don't believe that this is an issue that should be in our constitution", he said.
At its first cabinet meeting of the year yesterday the government spent two hours debating the recommendations of an Oireachtas committee.
Speaking alongside Flanagan, Enterprise Minister Heather Humphreys said she wished to speak wither her constituents further, adding that it is "a very complex and emotive issue".
However, Minister of State at the Department of Finance Patrick O'Donovan said he had a "different view".