Fianna Fáil ministers say the party's polling is "disappointing" and a "poor reflection of hard work" as they consistently struggle to strike a chord with the public.
The weekend RED C polling putting the party on 12% has come as a blow to TDs who are now trailing behind Fine Gael and Sinn Féin on 33% and 30% respectively.
Minister of State for Disability Anne Rabbitte told the: "I'd be lying if I said I haven't paid much attention to it. It's a poor reflection on hard work.
"I have always been critical of our communication, however, I expect that if we are missing a skill - messaging is essential at the moment.
Minister of State for Trade Promotion Robert Troy said the results were "disappointing".
Éamon Ó Cuiv says that the party are running "consistently behind" Fine Gael and Sinn Féin and need to consider how they manage the narrative.
"More worrying for us is Sinn Féin and Fine Gael are significantly ahead and we're not," he said.
"The circumstances we're in, if you want to change the narrative, we have to think long and hard about where we position ourselves.
"Micheál Martin presumes he will overtake one of them to become second biggest party but that remains to be seen."
Fianna Fáil TDs say recent scandals involving Tánaiste Leo Varadkar's leaking of a confidential document and the appointment of Supreme Court Judge Seamus Woulfe has made their party look weak.
"That shows they're outplaying us," says one Fianna Fáil TD.
"Leo does something wrong and we end up shouting and roaring at a parliamentary party meeting about it."
At one heated meeting, Mr Martin was branded “a disgrace” by Sligo-Leitrim TD Marc MacSharry, who accused his leader of being the cause of the poor polling.
One TD said the outburst was "harsh, but not a million miles off".
"We're losing our identity here. People talked about the Greens as the mudguard in this government, but it's us who's doing that," the TD said.
Clare TD Cathal Crowe said: "All parliamentary parties like to say that polls don't matter but, of course, we do look at them.
"We've seen a number of polls from 19% to 11%. I'd like to say they don't bother me but they do, all elected reps consider polls.
"We get a boost as a party to see you're performing well, and likewise it makes us look inward."
There have been rumblings within the party about a leadership challenge for months with one TD pointing out that Micheál Martin "moved on Brian Cowen when we were a lot higher than 11%".
"Fianna Fáil is finished if Micheál Martin remains beyond next summer, to be honest, I think it’s too late in any event," the TD said.
"He has qualities suitable to an era long since gone. We live in a sound bite world and he can’t compete.
Another TD said that it was likely Mr Martin would carry on as Taoiseach until the handover to Fine Gael in December 2022, but would not go further.
"When there are more TDs against him than for him, he'd be told and his exit managed. He deserves that much, at least."
Meanwhile, Dublin TD Jim O'Callaghan has done little to dispel the notion that he would be tipped for the top job in any event of a challenge after rejecting a seat at the cabinet table and speaking out against government policy in public.
Mr O'Callaghan told media over the weekend that he would be interested in the top job and would not rule out working with Sinn Féin in the next government, despite his issues with the party.