A poll shows that Leo Vardakar is currently the most popular choice to replace Enda Kenny as Fine Gael leader.
The poll, published in this morning's Irish Times, follows a turbulent week in the Dáil after Independent Ministers voted against the rest of the Government to support an abortion bill put forward by Wexford TD Mick Wallace.
Joe O'Toole also announced his resignation as chairman of the expert commission on water charges.
The Independent TD Mattie McGrath thinks Government cohesion may have been damaged by this week’s events.
However, he also thinks there is unlikely to be a heave against Enda Kenny in the short term as no politician currently wants to face into a General Election.
“I don't think there’ll be a heave, I think there is more nervousness in case there’s an election,” said McGrath.
“They don’t want to go to the country - no one does, including myself.
“There’s a lot of unease. I think the next two weeks are going to be a very testing time and if we get over those two weeks the summer might cool off things, but it’s going to be a very trying two weeks.”