By MAKIYA SEMINERA

Vital federal funding is on the way for Head Start centers that were thrown into crisis by the government shutdown, but it could take time before some children who rely on the federal program can return to preschool.

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Some centers that missed out on federal payments had to furlough staff. Others had to shut down entirely, destabilizing thousands of needy families around the country. And operators fear it could take weeks more for overdue payments to be processed.

Even when agencies receive long-delayed grant money, centers will have to rehire staff members and bring back families — both of which may have grown wary of instability in the program, which relies almost entirely on federal grants.

“The damage has been done in a lot of ways,” Massachusetts

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