It comes as the Health Minister is embroiled in the ongoing trolley crisis across Irish hospitals.
An online petition calling for the resignation of Health Minister Simon Harris has gained over 3000 signatures in 48 hours.
It highlights the overall state of the Health portfolio as well as the handling of the trolley crisis and the construction of the National Children's Hospital as key failings of the Minister.
Key Independents including Roscommon/Galway TD Dennis Naughten say they're still considering whether to support the motion.
Aontu leader and Meath/West TD Peadar Tóibín is behind the petition.
He says it's time politician's in Ireland were held to account: