The surprise promotion of Green Party Senator Pippa Hackett to a "super-junior" Cabinet post has enraged some of the party's other nine TDs who did not make the Government first team.
There are also questions about the appointment of Cllr Vincent P Martin, brother of the party deputy leader Catherine Martin, and Eamon Ryan loyalist Cllr Róisín Garvey, to the Seanad as the party's choices among the Taoiseach's 11 nominees.
Senator Hackett, who joins government via a device used only twice in the last 80 years, has been named as Junior Agriculture Minister to the senior minister Barry Cowen of Fianna Fáil, who is her constituency rival.
The Offaly organic farmer was first elected to the Seanad in a by-election last November without opposition from Fine Gael and Fianna Fáil. She was off the pace for a Dáil seat in Laois-Offaly, with 3,494 first preferences in February's election, but won a Seanad seat on the agricultural panel in elections in April.
Taoiseach Micheál Martin, on the prompting of Green Party leader Mr Ryan, named her on Saturday as one of three super-junior ministers entitled to attend Cabinet meetings.
He invoked a little used device in the 1937 Constitution allowing a maximum of two senators join Cabinet, which was last used in 1981, and only once before that in 1957.
Ms Hackett was a "Ryan loyalist" in the incipient election contest involving deputy leader Catherine Martin, and some anti-coalition party members in particular have railed against her appointment.
Just three of the party's 12 TDs have so far made it to the Cabinet table while nine who got a Dáil seat - some with a longer track record of party service - were overlooked and feel they were "leap-frogged".
But party sources dismissed suggestions that the appointment had anything to do with the leadership contest or the debate over coalition.
"Pippa Hackett is a farmer who understands issues like the farm-incomes crisis. She is best placed to ensure farm families' needs are addressed on issues like tackling climate change," one party source told the Irish Independent.
Others in the party also brushed aside suggestions that the choice of Cllr Garvey, from Clare, a staunch defender of the party leader, and Cllr Vincent P Martin, of Kildare North, a brother of the deputy leader, had anything to do with party machinations.
"These appointments were based on electoral performance in the Dáil votes. Both nominees polled over 5,000 votes each and were unlucky on the day not to make the Dáil," another party source said.
Vincent P Martin is also a senior counsel who will be available to advise the party on legal issues and legislation in particular.
Both he and Ms Garvey polled more first preferences than some of the party's 12 TDs who were successful in their Dáil bids.
The Seanad was only twice used to appoint ministers. In 1981 Garret FitzGerald appointed Professor Jim Dooge as foreign affairs minister due to tight Dáil numbers.
Before that in 1957 Éamon de Valera nominated War of Independence icon Seán Moylan to the Seanad and appointed him to cabinet after he lost his Dáil seat.
As acronyms go, DMTACSG, isn't a very good one and it's unlikely to catch on when people are describing the government's new Department of Media, Tourism, Arts, Culture, Sport and the Gaeltacht.
You'd be hard pressed to find someone in Fianna Fáil with something negative to say about its deputy leader Dara Calleary. The Mayo TD goes out of his way to get on with everyone. It is one of the reasons Micheál Martin appointed him as his deputy in 2018.