The education minister has been accused of exacerbating tensions with teaching unions after she claimed they have refused to accept public health advice.
Opposition and Government TDs called on Norma Foley to not speak publicly until after a full agreement is reached to get children with special educational needs back into classrooms.
Fianna Fáil's Eamon Ó Cuív and Fine Gael TD Kieran O'Donnell both suggested that Ms Foley should go into a Brexit-style "tunnel" to hammer out a resolution.
"My plea this evening would be to everybody now, all the parties to go into the tunnel and just sit down and see how this can be worked out in the interest of those probably least well able to speak for themselves and that's the children," Mr Ó Cuív told the Dáil.
Independent TD Thomas Pringle suggested that both Ms Foley and Minister of State for Special Education Josepha Madigan should resign.
"To say that the handling of the reopening of schools has been an omni-shambles would be the understatement of the year," the Donegal TD said.
He told Ms Foley that the attempt to pit parents against teachers, SNAs and unions is "reprehensible" and is "a blatant attempt to deflect from the fact that you have done nothing to plan for this since September, except to take advantage of the goodwill of all educational staff ".
Labour's Aodhán Ó Ríordáin said both Ms Foley and Ms Madigan have "lost control of the situation". He also said: "every time the minister gets an opportunity ...to speak about this issue she only makes things worse".
Ms Foley said her Department has prioritised the reopening of schools and classes for children with special educational needs and has "engaged intensively" with all stakeholders to realise this shared ambition.
She said the Department wrote to special schools and primary schools on January 15, setting out details of the framework to allow in-school teaching and learning take place.
"This guidance was agreed with the Into and Forsa," she said.
Ms Foley said Ireland is now an outlier in the European Union in not having in-person provision available for students with special educational needs.
"We have addressed the concerns raised in relation to safety, including making public health officials available to education partner representatives, and subsequently facilitating three of the most senior public health officials in the country to communicate directly with teachers and SNAs."
She said: "The Department has consistently accepted and implemented the knowledge and advice of public health. This is the first time that unions have refused to accept that advice."
Ms Foley told the Dáil that "all discussions" around the opening up of schools "happened first" and public announcements had followed.
Independent TD Mattie McGrath said certainty is now needed and after two failed attempts to get children back to school he said "there can't be any more false dawns".