Tory leader Ruth Davidson urged the First Minister to dump the policy after a powerful Holyrood committee effectively blocked it.
A bid to save the scheme, which will assign a Named Person for every child, was left in tatters on Wednesday when MSPs voted to withhold their support until John Swinney provides a detailed code of practice.
The Deputy First Minister has claimed he cannot publish crucial rules until September next year and it could now take until 2019 to secure Parliamentary approval.
The Children and Young People (Information Sharing) (Scotland) Bill was set to go before Holyrood’s chamber before the end of this year.
But the education committee voted against publishing a stage one report, meaning the legislation cannot proceed.
Attacking the government, Ms Davidson told the First Minister the policy “is a mess and it’s only her and the Deputy First Minister that can’t seem to see it.”
She added that while “everybody wants protection for vulnerable children” it was “now clear that Parliament has joined the public in no longer having confidence in these plans.”
Challenging Ms Sturgeon during her weekly question session, Ms Davidson said: “We should focus resources on those who actually need it rather than having blanket interference for every family in Scotland.
“We are willing to get round the table to find a fresh solution to this but first the First Minister needs to ditch this broken plan, because her named person policy in tatters.
“Can she simply concede that so we can all move on?”
But Ms Sturgeon insisted: “The Scottish Government will proceed with its named-person plans for the simple reason that they are in the best interests of children, particularly vulnerable children, across the country.”
The committee’s vote is the latest setback for the initiative after Mr Swinney was forced to overhaul his proposals after they were ruled unlawful by the Supreme Court last year.
The First Minister said she was “disappointed” with Wednesday’s decision and argued it was “unnecessary” to delay proceedings.
Ms Davidson also demanded that minutes for private talks on the policy should be published amid claims the the government tried to “lobby” witnesses before they give evidence to the committee.
“It’s usually organisations that lobby governments, not governments that lobby organisations,” she said.
But Ms Sturgeon said: “It is our duty, as the Government, to listen to the concerns that such organisations have and to seek to address them.”