The Sinn Féin leader Mary Lou McDonald has said that Phil Hogan 'dug his own difficulties' in relation to the golf gate scandal.
It comes as the Government leaders said the EU trade commissioner 'clearly' breached public health guidelines on a recent visit to Ireland.
While Taoiseach Micheál Martin said Mr Hogan undermined Ireland’s public health guidelines, but has refused to call for his resignation.
Any such final move would come from European Commission said President Ursula von der Leyen, who said she had 'taken note' of the Government's rejection of the commissioner’s defence against claims he repeatedly broke COVID-19 restrictions.
Ms McDonald told The Hard Shoulder: "What I want to see above all else is that we move beyond now the absolute chaos and shambles that we've witnessed in the last week in particular.
"I think that Phil Hogan's position now to my mind is untenable, given that the current Government - the Taoiseach, the Tánaiste, the leader of the Green Party - have said that they have no confidence in him.
"I think he's in a very difficult situation, I think people are very angry and I understand why.
"When I saw the images or heard the story of this dinner in Clifton in Galway, my mind immediately went to the Galway tent of old - and the great and the good rubbing shoulders and that old politics of the old guard in Fianna Fáil and Fine Gael: politics that did not serve this country well and needs to be dispatched to the dustbin of history but still persists as we saw.
"That made me angry, I know it made others angry - and then there's the concern around the virus and the public health standards and so on.
"And I think in all fairness, Phil Hogan has dug his own difficulties even deeper and certainly the Government was confused at the outset.
"They said initially they had no confidence in him, and that was fair enough, they asked him to consider his position on Friday, they seemed to change their mind in the course of the weekend and into Monday.
"And now they are saying again that they have absolutely no confidence in him.
"So I think what needs to happen is they need to communicate with the President of the Commission - respecting of course that it is the prerogative of the European institutions to ultimately decide Commissioner Hogan's fate.
"But to me it's not plausible that having lost confidence in the very people who appointed him to his role that he would stagger on.
"And in any event, we cannot have the kind of chaos and mixed messages and messing, quite frankly, that we have seen over the last number of weeks.
"It's high time now that the Government got its act together."
She added that having Mr Hogan as a European Commissioner with regard Brexit is not a prerequisite.
"I have to record that Michel Barnier, who's led the negativing effort on the European side, in my view has acquitted himself extremely well.
"Certainly I have huge confidence in him to engage on the issues, I have found him to be consistent and honorable.
"And truth be told in the last round of negotiations, it was Michel Barnier - and by the way, not just him but a very accomplished team around him - who did most of the heavy lifting."
"So I don't accept the proposition that if Phil Hogan is not in place as a commissioner that all is lost in respect of Brexit".
"Of course we need a commissioner, of course we need somebody capable and competent in that role.
"But I tell you what we need above all else to mind us, to mind the collective interest of all of us who live on this island: we need a Government that is stable and that is not chaotic.
"And we need a government that's built around common purpose and direction - not one, as is the case now, it seems to be one that's built on rivalry and contradictions and - quite frankly - gross incompetence at the highest level".