Indulging in an over-long 'goodbye period' would cause far too many big problems for the country
Pat Deering has fixed the nearest thing we have to a timeframe. The Carlow-Kilkenny TD has said that he will table a motion of no-confidence at the weekly meeting of TDs, senators and MEPs at 5.30pm next Wednesday - unless Enda Kenny outlines the details of his departure.
"If Enda has not given an exit timeline before, or at next week's party meeting, then a very damaging all-out and ugly row will erupt," one seasoned backbencher, who has avoided the ranks of the awkward squad, summed up.
So far Mr Kenny has kept his powder bone dry on his intentions. After what was easily his most ramshackle week since being elected Taoiseach on March 9, 2011, he looked uncharacteristically tired and drawn.
There is a widespread assumption that he will stand down - and sooner rather than later. But assumptions are dangerously unreliable things in politics and we have heard nothing so far of the Taoiseach's intentions.
The obverse of the early departure assumption is the very real fear among some frustrated Fine Gael deputies, who believe it is past time their leader left, is that he is digging in for a fight. "If he did that, he could be hard to shift," says another Fine Gael insider.
Already, there have been warnings against reverting to the very bad old days described in the landmark television documentary 'Family At War'. Already, Senator Paul Coghlan of Killarney, has been on Radio Kerry warning that things were headed in that direction.
Senator Coghlan, a wily judge of politics, predicted that Pat Deering's no-confidence move would not succeed. It's a view widely shared - but it is early days yet as most denizens of Leinster House prepare for another week of waiting.
Mr Kenny's behaviour on Thursday night caused major alarm in Fine Gael. He refused to even acknowledge that there was a question about his continuing as party leader and Taoiseach. Instead he cited a long list of engagements in the coming weeks and put great stress on the need to advance lobbying on the Brexit issue.
Yet any way you look at things we are really discussing when and how Mr Kenny will go. Some within Fine Gael fear the Taoiseach may be keen to linger until the summer recess.
A summer departure has been mentioned since the Fine Gael party had its pre-Dáil meeting in Newbridge last September. It had a ring of truth to it until the debacle that befell Mr Kenny and his colleagues over the past week.
These events crystallised many Fine Gael TDs' thoughts. Mr Kenny is now doing them continuing reputational damage and a general election is only another stumbling crisis away. They cannot risk having to go to the hustings with him as leader.
For them the leadership change must be addressed and quickly. The impatient ones are looking at the recess around Easter which could allow them to complete a leadership election. Easter Sunday is on April 16 this year.
But you can pick from a clatter of other dates that are being cited for various reasons in all of this. There is the St Patrick's Day visit to the White House around March 17 and on March 9 he will have served six continuous years as Taoiseach. Then there is April 20 when he overtakes John A Costello's term as the longest-serving Fine Gael Taoiseach.
There is a bigger reality at play here. The Brexit issue, which has lingered as a persistent threat since the British referendum result on June 24 last, is now about to come to the boil.
British Prime Minister Theresa May will trigger the Article 50 exit process on March 9. We have to know what is happening about the office of Taoiseach and the leader of the largest political party as quickly as possible.
Anything less will foment continuing uncertainty in Ireland. Yes, the Taoiseach does have good personal contacts across the EU built back over the years.
But the heavy lifting in these crucial negotiations will be done by Irish diplomats. A new Taoiseach will have to begin cultivating his or her own EU relationships. Let's recall that the day after his own election as Taoiseach, Mr Kenny headed in to a crucial summit, his first ever, which dealt with Ireland's bank debt.
Mr Kenny is entitled to a dignified period to exit Government Buildings. A formal end just after the Easter recess would be acceptable. But hanging on until after April 20 for sentimental reasons is not acceptable and dragging this business up to the summer is unthinkable.
Indulging in an over-long "goodbye period" would cause far too many big problems for the country at a time we can ill-afford it. The public were already losing patience with the Dáil fiasco as this past week ended. Their scarce stock of patience will be pushed too far by more delays.
Some see Mr Kenny's silent defiance as "mischievous", others see it as petulance.
"After over 40 years in the Dáil he's not about to be told what to do by some whippersnapper there a few wet weeks," one Fine Gael veteran says.
Whatever the Taoiseach's motivation, it is clear that his stance has hobbled the two succession frontrunners, Leo Varadkar and Simon Coveney. Neither can be seen to be pushing Mr Kenny too hard and too fast to pack up and go. Both have with careful piety spoken of giving the Taoiseach time space and dignity. The threat of a backlash is more immediate in Leo Varadkar's case.
The outspoken ones expressing impatience are seen as "Leoites". He insists he has nothing to do with their "Enda go" statements and he may be right.
But it does not look great and there are those who fear it may alienate the party middle ground and Mr Kenny loyalists who might have been prepared to swing in behind Mr Varadkar. "This contest is still Leo's to lose - but we'll have to see if there is any negative blowback from the calls for Enda to quit," one TD says.
The contest is rapidly coming down to a straight battle between Varadkar and Coveney, with Varadkar perceived to have the advantage, but nobody is underestimating Coveney's battling powers just yet.
But the surreal part is that the contest cannot begin until Enda Kenny moves. That must change lest Fine Gael return to civil war.