Right now a third of voters want the Dublin West TD to take over from Enda Kenny – that's twice the popularity of the next choice Simon Coveney.
The third name offered to voters, by Behaviour and Attitudes researchers, was that of Justice Minister Frances Fitzgerald, but she has only 12 per cent support.
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The results from the poll, which was carried out between the 4th and 14th of this month, are published in today's Sunday Times.
A seperate B&A poll out today shows that overall support for Fine Gael remains unchanged on 24 per cent.
Political Correspondent for the Sunday Times, Sarah McInerney says the party will not be pleased