Lord Carey and Lord Williams have called for a re-think of the policy, which they claim will hit the low-paid the hardest.
Mr Carey told The Sun newspaper that he himself relied on government support while bringing up his four children, and knows first hand what damage the proposed changes to tax credits could cause.
He said: "I support the aim of the government to make work pay and put in place a reasonable cap on welfare pay.
"But I urge the government to reconsider these cuts to working tax credits that will hit many hardworking families very hard.
"I well remember as a young poorly-paid clergyman needing the help of the state in the form of family income support.
"So there is nothing new about government support for low-paid families."
And Lord Williams said: "They are inflicting heavy damage on hard-working families.
"It ought to be common sense and compassion."
However David Cameron says changes such as free childcare mean that families with children will be better off.
The Treasury said: "It's vital we have a lower-welfare, lower-tax, higher-wage economy."
