She said the PPTA would be seeking compensation for members for "the hurt, humiliation and financial suffering caused by the dysfunctional payroll system".
"Continued Novopay errors mean schools, students principals and administration staff are at the end of their tether," Mrs Roberts said.
Mr Joyce has ordered a draft technical audit to determine if Novopay's flaws are "terminal".
The Australian provider of Novopay, Talent2 rolled out the first of three software upgrades over the weekend.
PricewaterhouseCoopers confirmed 628 schools were involved, with 552 staff not paid as a result of problems with Novopay - 589 were underpaid and 521 were overpaid.
More than 800 calls were made to both the Education Ministry and the contact centre.
The PPTA are expecting to receive details of a survival package for schools at a Education Ministry briefing on Thursday.
The union is still deciding if the legal action will be taken against the Government or Talent2.