Baby P died after suffering months of abuse
One in seven social worker posts across England is unfilled as a "real crisis" grips the profession, the Tories say.
They say figures suggest a third of posts were unfilled at several councils in November 2008 - just before the Baby P abuse case became public.
Tory spokesman Tim Loughton called for a new post of "chief social worker" and a huge recruitment and PR campaign.
Minister Ed Balls said a new taskforce would look at barriers faced by social workers and recommend long-term reform.
The Conservatives are using their "opposition day" debate in the Commons to discuss the "unacceptably high" levels of child abuse and deaths at the hands of carers and parents.
Mr Loughton told BBC Radio 4's Today programme there could be more cases like that of Baby P - who died aged 17 months after sustained abuse - if the shortage was not addressed.
He said a new post of chief social worker should be created to speak up for the profession, high-performing social workers should be encouraged to take on the most challenging areas and bureaucracy should be reduced.
The problem had been getting worse but it took tragedies like the Baby P case to flag up the fact there was a "real crisis" in the profession, he said.
He said social workers were "very easily panned in the media" but added: "The vast majority of social workers actually do a good job and the vast majority of children in the care of local authorities don't end up like Baby P.
"We need to improve the image and status and standing of social workers. They should be seen in just the same way as we view doctors, teachers, nurses or police. We need a massive recruitment and PR campaign."
The Conservatives' figures, obtained under the Freedom of Information Act, suggest that across England the national vacancy rate is 14%, up from 11% in 2005.
Haringey, the north London council criticised over the death of Baby P, last week asked other local authorities to lend it social workers to tackle a staffing crisis.
Unison, which represents 40,000 social workers, said it had already warned that the shortage represented a "ticking time bomb" and called on councils to take urgent action.
General secretary Dave Prentis said: "It's a bit rich for the Tories to start whingeing about the crisis in recruiting and retaining social workers when they run most councils.
"The answer to the problem lies in their hands. They could start by sorting out local government pay."
Margaret Eaton, chairman of the Local Government Association, said councils had difficulties getting high calibre social workers for children. She added: "It is a tough job to do and for councils it is the toughest job to fill."
Children's Secretary Ed Balls said a review of social service departments across England announced in December would include a new task force to identify "barriers" social workers face in their jobs which would recommend long-term reforms.
"Social workers do a really difficult job, often in extremely challenging circumstances and they have a vital role in protecting children and young people from harm," he said.
But he claimed a Conservative government would cut £300m from children's services this year - equivalent to £2m for every children's services department in England.
And he said their opposition to ContactPoint - a £224m database containing the details of every child in England - suggested they were not serious about child protection, as it was recommended by the Laming inquiry into Victoria Climbie's death.
The database is intended to improve information sharing between professionals working with children. But the Conservatives have argued it is an "expensive data disaster waiting to happen" and say there are no guarantees "inappropriate people" would not be able to access it.