One TD claims the situation has highlighted dysfunction in the HSE
It has emerged since Vicky Phelan took her case, another 30 women have commenced legal action because of the Cervical Check scandal.
The Health Service Executive (HSE) also admitted a further review is likely to show that even more women were not told about the audit of their cancer smear tests.
Management also said the health service is doing everything to help the inquiry into what happened.
Labour TD Alan Kelly said the situation has highlighted the dysfunction in the HSE.
"Now if there's ever a kind of row of events that symbolises my view of arse-covering in the HSE, it's this.
"Multiple arse-covering which now many people in the HSE feel they have to push everything up the line, instead of taking responsibility themselves, in case their own managers ever land them in it".
The chairman of the Public Accounts Committee (PAC) said we need "clean hands" in the management of the Cervical Check programme.
Sean Flemming said he hopes the chief executive of HSE takes charge, and appoints a new team to deal with the crisis.
"The people who were involved in the management of the Cervical Check programme are part of the problem - and they're certainly not part of the solution.
"They may have historical information, but going forward we need people coming to the table with clean hands who are not having a vested interest in covering or trying to put right at this stage what happened in the past".
Fine Gael's Kate O'Connell said the management of the HSE, the State Claims Agency and Cervical Check should be sent packing.
Reacting to a lack of information on what happened, she claimed the HSE is not fit for purpose.
"We're dealing with a population the size of Manchester - for normal people looking in, this is madness - this is dysfunction, this is a system to my mind that is rotten to the core (and) not fit for purpose".