While the party's candidate David McGuinness was always going to be up against it to take the seat, given he only received 623 first preferences in February's election, senior party figures have said that any faint hopes are now gone.
The battle for the seat formerly held by Mr Lenihan has been seen to date as a fight between Labour rebel candidate Patrick Nulty and Ruth Coppinger, the glamorous Socialist Party candidate.
However, Fine Gael is claiming it could be poised for a surprise victory in the Dublin West by-election. Based on party polls, its candidate Eithne Loftus is in contention and Fianna Fail may be the party which will sweep its old rivals across the line.
This has been dismissed by Labour and the Socialist Party after some less than impressive media performances by Ms Loftus.
However, while Mr Nulty is still the narrow favourite, the battle between Fine Gael and Labour will be decided by the capacity of the parties to get their respective core supporters to vote. Fianna Fail and Sinn Fein transfers may also play a critical role and the research by Fine Gael suggests that transfers from both parties will slightly favour the Fine Gael candidate.
David McGuinness's failure to take the seat will mean Fianna Fail will be left without any Dail representation in the capital. If the poll is replicated, the party is poised to retain a similar level of support to that secured in the recent general election, which will be of little comfort to leader Micheal Martin.
Sinn Fein, which has traditionally been outdone by Joe Higgins and the Socialist Party in what should be a natural constituency for the party, is not polling at all well. Its candidate, Paul Donnelly, is not in contention for the seat, the polls suggest.
The Labour hierarchy have continued to express confidence in Mr Nulty even though he voted against the Programme for Government at the party's conference in February.
Fine Gael sources maintain that Ms Loftus is securing a great deal of the support that had formerly gone to Mr Lenihan.
They claim this shows "the middle classes in Castleknock and Laurel Lodge support what the Government is doing'' and added "there is an element of a referendum on the Government surrounding it".
Though the first victory for a government candidate in 21 by-elections would improve the morale of the Rainbow, should Fine Gael defeat Labour in a constituency that is part of Labour's perceived heartland, pre-budgetary tensions between the parties would likely intensify.
One source noted that the result could even have significant consequences for relations in the Cabinet: "This is a battle of the big beasts which will decide whether Minister Leo Varadkar or Minister Joan Burton will have the bragging rights in Dublin West."
In total, there are 13 candidates seeking the seat with a host of non-party candidates.