So will the Green Party join a coalition with Fianna Fáil and Fine Gael?
The answer turns on a second question: Are the two big parties ready to be seen to concede enough tough Green Party policy demands which are bound to hurt their own traditional grassroots' support?
Soon after the election count ended on Tuesday, February 11, speculation promptly switched to the prospects of a Fianna Fáil-Fine Gael-Green coalition. It was based on pure Dáil arithmetic; the realpolitik that the two big parties did not want to deal with Sinn Féin; and the Greens' record of staying the course through a very fraught first period in coalition from 2007 until 2011.
But back in mid-February, as that three-way coalition speculation was rife, this writer spoke with somebody who knows much about the current realities of Irish politics. "For the Green Party to do a deal with Fianna Fáil and Fine Gael, the two big ones will have to make serious concessions to the Greens - and be seen publicly to do that," the observer noted.
That comment holds good today as the Green Party's 12 TDs, two senators and two MEPs now contemplate their next move.
For now they have very reasonably sought more information - and it is likely they will open dialogue on government formation. But that is very far from saying the Green Party will join this coalition.
Back in 2007, when an experienced and united Green Party joined government with Fianna Fáil, they were "wanted but not necessarily needed".
This time around the 12 Green TDs are "both wanted and needed".
Along with Fianna Fáil's and Fine Gael's combined 74 TDs, the Greens would take the number to 86 Dáil seats, comfortably above the required majority of 80 TDs.
Add a few usually reliable Independents and there is even a margin for some "walkouts" from government over this or that flashpoint.
So, for sheer numbers, Micheál Martin and Leo Varadkar view the Greens as "the big prize". But unlike 2007 the Green Party - 10 of whom are relative newcomers to elected politics - are deeply divided on the issue of this coalition.
It is clear party leader Eamon Ryan is open to returning to government but faces an uphill battle to convince his colleagues.
Let's recall that some kind of membership vote will have to be organised, possibly via the post, and needs a two-thirds majority.
There is little mystery around the things Fianna Fáil and Fine Gael must concede.
The Green Party's key issue is tackling climate change and it wants to know how a government can deliver a more than tripling in yearly reductions of carbon emissions to 7pc. It also wants to know that houses will be built in big numbers.
In a similar vein it wants a 2:1 ratio in transport investment in favour of public transport.
The Green Party will come under huge pressure to act in the "national interest". But it will try to turn the questions on Fianna Fáil and Fine Gael.