The Health Minister Leo Varadkar has said Enda Kenny is leader of Fine Gael "for as long as he wants to be".
It follows a new Millward Brown poll for the Sunday Independent, which found that 72% of people believe his coming out as gay will not damage his chances of becoming Taoiseach.
Voters were also asked how they plan to vote in the same-sex marriage referendum and the response was an emphatic Yes - with 62% claiming they will vote in favour of it, 16% say No and almost a quarter do not know.
It was not the only controversial question that was asked: When it comes to abortion, over half the population wants a referendum to decide if we should repeal the 8th amendment.
On water charges, 40% say they will definitely pay the bills, 30% say they definitely will not.
Meanwhile, satisfaction with the government goes up four to 23%, while the four main party leaders see their satisfaction with voters also go up.
The poll shows how people feel about the main political parties too - showing Sinn Féin as the most popular party in the country, with gains for others at the expense of Independents.
Fine Gael go up 3 points to 25%, Fianna Fáil on 19% is up 1 point, and Labour goes up a similar amount to 5%.
Independents take all the losses, down 9 to 23%.
Mr Varadkar told the Sunday Show here on Newstalk that he does not pay too much attention to the polls - and that the Taoiseach's position is safe.
On the issue of the Jobstown protests, which saw several arrests, Mr Varadkar says he supports peaceful protests, but not "vicious abuse".
The Health Minister said the crisis in our emergency departments is a result of seven years of budget cuts and freezes.
Leo Varadkar says he is unhappy with the progress being made in relation to the issue of overcrowding, and admits a lot more needs to be done over the coming months to open beds and expand capacity across the health service:
And the minister says the government is already considering its options when the Haddington Road agreement comes to and end.
You can listen to Leo Varadkar's full interview on the Sunday Show below:
