Sinn Féin's health spokesman claims issues around Tony Holohan's new role saw the Taoiseach step in to do the Health Minister's job.
David Cullinane was speaking after Micheál Martin said the process should be paused and reassessed.
Dr Holohan is leaving his post as Chief Medical Officer to take up a position with Trinity College Dublin (TCD).
However the change is an open-ended secondment, rather than a permanent move.
As such the Department of Health is to continue paying his salary of more than €187,000 - even though he will not be working there.
Deputy Cullinane told The Hard Shoulder Mr Martin had to step in when Health Minister Stephen Donnelly did not.
He says generally a secondment means a temporary situation - but this is not the case here.
"What we've being told is that this is a permanent transfer, that the CMO is leaving his post, is stepping down, will not be returning.
"And I think what caught people by surprise is that nobody in Government was aware of this.
"The Minister for Health was not aware of the process - in fact he doubled down on the process, even though he was kept in the dark.
"I think there are real questions now for the Minister for Health because it seems to me that it took the Taoiseach to step in to pause a process when in fact the Minister for Health had failed to do so.
"He didn't see the issues in front of him, as far as I can see.
"It's never a good thing when the Taoiseach has to come in and do the job for the Minister for Health for him."
Mr Cullinane says the position itself is not in dispute.
"I think in the first instance we need to know who was responsible for the process.
"We did learn yesterday at a meeting of the Oireachtas Health Committee, directly from Dr Holohan, that he himself was involved in discussions in relation to the process of the position itself.
"The professorship that has been created in fact is a good professorship, from my perspective.
"But there are issues in relation to the secondment, and whether or not it is a secondment".
'Questions here for Robert Watt'
Deputy Cullinane says an announcement that Dr Holohan was stepping down as CMO was unclear.
"It made it very clear that he was stepping down, it made it very clear that he would not be coming back.
"And bizarrely we found out that the Department [of Health] is now paying for his full salary while in Trinity - which we know is a substantial salary on top of what the professorship salary is in Trinity College".
And he believes the secretary-general at the Department of Health, Robert Watt, also has to answer questions.
"What was even more bizarre is at a different meeting of the Health Committee on Wednesday, Robert Watt was before a public session... was asked all of these questions, he did not answer the questions to anybody's satisfaction.
"So obviously there are questions here for Mr Watt.
"There was a cosy deal done to put into the Department of Health, which I believe was a mistake.
"And I believe that he has now signed off on a process which is also a mistake".