In a survey to be published today by the Scottish Parent Teacher Council (SPTC), 74% per cent of parents said they were either "not content" or "very unhappy" with the idea proposed by the Scottish Government.
More than 80% said they felt the move to appoint a "Named Person" - typically a teacher or health worker - would not help their child.
The proposal is contained in the Children and Young People (Scotland) Bill currently going through the Scottish Parliament. Only one in five respondents to the SPTC survey of 400 parents said they were happy with the scheme as proposed.
Eileen Prior, the SPTC executive director, said: "This survey was designed specifically to sound out parents on the issues we have identified as worrying in the Bill. The majority of those who responded echoed our concerns but many sadly felt ill-informed about the proposal."
She added: "We take the view that most children thankfully already have a 'named person' - their parent or carer. The proposal implies every child is at risk, and every family is struggling, which we know is not true and in fact undermines the role and responsibilities of parents.
"There is much in the Bill to support, but we believe this proposal is ill-considered, wasteful and potentially destructive."
Liz Smith MSP, the Scottish Conservative spokeswoman for young people, called the proposal an unnecessary and potentially expensive intrusion by the state into family life and one that threatened to divert resources away from vulnerable children.
"The results of this survey confirm the extent of the concern among many parents about the Scottish Government's proposals," she said.
"The SPTC has rightly questioned why the state has the primary obligation to look after children, when there is an implicit understanding in other legislation that the main responsibility lies with parents and families."
The SPTC has also raised concerns about the proposals for information-sharing about parents and children between health and social services professionals, and the possibility that these may run contrary to individuals' rights to privacy.
These worries have been echoed by the Faculty of Advocates and the Law Society of Scotland. In a written submission to the Education and Culture Committee, the Faculty warned about the "potentially insidious aspects" of the Bill, specifically the area of state intervention into family life.
The Bill was introduced by Health and Wellbeing Secretary Alex Neil in April and stage one is expected to conclude on November 29.
The Named Person would offer advice, information and support to the child and their family, help them access a particular service or support, and co-ordinate with service-providers or local authorities on the child's behalf.