It has already been dubbed "the doomsday scenario" and last night it was discussed on the margins of a meeting of party leaders in Government Buildings.
It centres on what happens if Dáil Ceann Comhairle Seán Ó Fearghaíl and President Michael D Higgins become incapacitated as a result of the coronavirus. With no Leas Ceann Comhairle as yet elected by this Dáil, the Presidential Commission, which performs the functions of Mr Higgins in the event he is unable to, would not be able to sit. It is the very definition of a constitutional crisis.
Last night, the Taoiseach is understood to have approached Independent TD Denis Naughten, who unsuccessfully challenged Mr Ó Fearghaíl last month, about becoming the Dáil's deputy chairman temporarily. "It's a doomsday scenario," said a source. "The proposal was to set aside standing orders until the end of September and appoint an agreed Leas Ceann Comhairle until then."
But Mr Naughten's name was vetoed by other party leaders and now the matter goes back to the Dáil business committee on Thursday.
Mr Varadkar's proposal hit the rocks on a day when it became apparent that even as the greatest public health crisis the State has ever faced worsens, the political consensus around how to respond to it has shattered.
The party leaders' meeting lasted some two hours with various officials briefing on the state of play.
TDs' gripes about testing and personal protective equipment (PPE) shortages were addressed by HSE boss Paul Reid who gave assurances that huge orders of PPE and testing kits were on the way.
The Government briefed on further supports likely to be announced for the unemployed today, but with no specifics as officials work overtime to hammer out the detail.
As many businesses report that insurance companies are rejecting their claims for loss of business, the Taoiseach was said by three sources in the meeting to have noted that if every business claimed for their premises being forced to close, the insurance industry wouldn't be able to cover the cost. The realities of this crisis are hitting home every day.
Earlier, the practical difficulties of enforcing social distancing were evident as the Taoiseach and the Health Minister arrived at the offices of the charity Alone in Dublin to meet those running a special Covid-19 helpline for the elderly. "That's not two metres," said Simon Harris as he passed journalists straining to keep away from him. "I'm not sure two metres is going to work," Mr Varadkar observed.
Whatever about social distance, all the leaders were keen to put political distance between themselves and their opponents.
At Leinster House, Sinn Féin's Mary Lou McDonald called for a shutdown of all non-essential businesses. But Mr Varadkar signalled earlier that while further restrictions were likely to be announced today, a full lockdown was not.
Fianna Fáil leader Micheál Martin called for more detail on where in the country there were clusters of coronavirus cases, more support for businesses and for the State to cover 75pc of wages for workers made redundant in recent days. But it was notable that he broadly aligned with the Taoiseach in the belief that a full lockdown was not necessary.
It was evidence once more that the slow march towards an historic FF-FG government continues. Talks on that continue this week. Mr Martin said "there is very little in terms of a programme for government" hammered out.
But how can there be when this crisis is increasingly likely to become all-consuming for the next administration?