About 200 social workers in the metropolitan district covering Huddersfield and Dewsbury are planning a 24-hour strike on Tuesday, possibly followed by a 48-hour stoppage in the following week.
Paul Holmes, the Unison branch secretary in Kirklees, said: "If there are any serious cases involving children, we expect managers to cover."
The row centres on a £900 annual pay increment that the staff claimed in 1999 to keep pace with social workers in Wakefield, Leeds and Bradford. Mr Holmes said the authority agreed to pay the increment in March when it realised it was losing staff to other districts. But it rejected the claim that the money should be backdated to 1999.
The union balloted for strike action after the authority introduced the increase last month, with backdating to October 2000.
Mr Holmes said: "The council's chief officers regraded themselves at the start of 2000, taking an £8,000 annual increase backdated to 1999. What's sauce for the goose is sauce for the gander."
Philip Cotterill, the council's director of social affairs and health, said he was optimistic strikes could be averted by a fresh offer to staff on Monday.
He said there were "robust contingency plans" to protect children at risk.
