Social Protection Minister Regina Doherty's position in the Cabinet has been called into question by the Social Democrats over the public services card scandal.
Social Democrats co-leader Roisin Shortall said Ms Doherty and other ministers involved in the situation may need to step down due to the "unprecedented" stand-off with the data protection commissioner.
Late last month, the data protection commissioner Helen Dixon said the Government's use of the public service card was unlawful and recommended it be scrapped.
After considering the demand, Social Protection Minister Regina Doherty said this week the Government will not be publishing Ms Dixon's report and confirmed it will instead appeal the decision.
Asked about the situation at the annual Social Democrats pre-Dáil think-in at the Rediscovery Centre in Ballymun, party co-leader Roisin Shortall urged Ms Doherty to re-consider the appeal.
And, underlining the severity of the issue, she said if the Government fails to back down then Ms Doherty may face calls to resign.
"I think it's unprecedented for a Government to challenge, legally challenge, an independent regulator, and I think it's ill-advised," Ms Shortall said.
"I don't know how this got this far. There's no business case for it, which is incredible when you think €60m has been spent on this and it's not just the minister for social protection, it is also the minister for finance.
"We would call on them to publish the report, they've been sitting on it for a year now," she said.
During the same media event, fellow Social Democrats TD Catherine Murphy said she has sent 60 parliamentary questions in recent years over the public service card issue.
Describing the Government's stand-off with the data protection commissioner as quite astonishing, she said essentially what the Government is doing in its use of the public service card "is not legal".
The Social Democrats pre-Dáil think-in also saw a focus on sustainable communities and environmentally friendly policies over the coming years.