The Taoiseach is unlikely to give a firm indication of his plans to step down as Fine Gael leader for several weeks, with his allies saying he should stay until the summer.
Minister for Finance Michael Noonan said on Monday Enda Kenny should remain until June, while other sources suggested a leadership contest should not begin until after the Dáil summer recess on July 13th.
Indications of these timeframes surprised many in the party, with senior sources saying they did not believe the succession process would be allowed stretch into June.
The Taoiseach had said he would deal with his future “effectively and conclusively” soon after his return from his St Patrick’s Day visit to the United States.
Mr Noonan told RTÉ News Mr Kenny's performance in Washington last week, particularly his widely-praised speech on immigration in front of US president Donald Trump, "shows how diplomatic he can be".
This illustrated why he should remain until Ireland’s Brexit negotiating position was concluded at “the end of May or early June”.
Mr Kenny is said to be extremely annoyed with the media coverage of his trip to the United States.
Those around him said the Irish press corps had been overly cynical and had to be prompted to give the Taoiseach praise by the reaction from international media outlets such as the New York Times and Channel 4 news.
Different note
Minister for Housing Simon Coveney had earlier struck a different note to Mr Noonan, saying he believed Mr Kenny would start the process to elect a successor “sooner rather than later”.
Mr Coveney also said it was widely expected Mr Kenny wanted to be present at the first European summit following the March 29th triggering of Brexit.
Within the party, there is a willingness to allow Mr Kenny to deal with the opening stages of the Brexit process, up to the summit expected in late April or early May to adopt guidelines for the negotiations.
Remaining longer would likely spark protests.
It is also understood Mr Kenny is unlikely to preannounce a resignation date that would be weeks in advance.
Rather, he will only announce his standing down when he is ready to do so, scotching suggestions of a lengthy period as interim Taoiseach.
This would mean the contest to succeed him would begin almost immediately upon his announcement, although he would remain as Taoiseach for the duration of the three-week leadership contest.
It was widely stressed, however, that only Mr Kenny and his family were likely to have a firm idea of his intentions.
One friend said Mr Kenny was probably “clear in his own mind” on what he wanted to do.
Mr Kenny had initially thought of stepping down in May, which prompted his statement to the Fine Gael parliamentary party last month, but this had been put back because of the delay in triggering Brexit.
Some TDs also said that even if Mr Kenny did not want to outline his plans to the party for a number of weeks, he would be challenged at parliamentary party meetings.