Albert Henderson, head of schools at Inverclyde council, said some support staff might end up out of work because of the squeeze on budgets from free meals.
But Mr Henderson and fellow council leaders said they broadly supported the plan, which could be implemented across Scotland.
They said some schools might have to curtail classes in the gymnasium if the sports hall was used as a dining hall, but that most would probably be able to implement the change without too much investment in new facilities.
Mr Henderson was giving evidence to Holyrood's education committee, which is investigating the Scottish Government's plans to introduce free school meals for all P1 to P3 children in Scotland.
Mr Henderson agreed extra resources were being made available for councils but said extreme pressures from elsewhere meant cutbacks were needed to fund the free meals.
He said councils would face "stark choices", and a "realignment" in Inverclyde's budget would be needed to cover the 368,000 cost of the scheme.
"If you were converting that into teaching staff, we're talking about ten teaching staff, so we may be faced with stark choices," he said.
And he added: "We might be faced with staff shortages and that might mean looking at support staff."
Mr Henderson said he would favour a more targeted approach on free school meals.