The independent Institute for Fiscal Studies has warned that 13 million families will lose an average of £240 a year when the cuts come into effect in April, while three million will lose £1,000 or more.
CARE said it had done research which found a similar burden would be placed on working families.
A family with two children and earning £25,000 per annum will be unlikely to have enough money to meet even the bare essentials, it said.
The charity claimed families could be hit with "an eye-watering 80% marginal tax rate" because of the new Living Wage.
CEO Nola Leach said: "Increasingly prominent voices are raising very real and genuine concerns about the Chancellor's tax credit plans.
"Three million working families face considerable financial misery from April 2016 as a direct result of the proposed changes and it is quite wrong that the burden of reducing the deficit is placed on them.
"We already have a tax system where income tax takes no account of family responsibilities so at the very least, if tax credits are going to be phased out, tax reliefs should be phased in for families.
"The eye-watering marginal tax rate means it is going to be very hard for families to compensate for tax credit losses through extra work and they now face a black hole in their finances when these changes come into force.
"The Chancellor must think again and his upcoming Autumn Statement is a perfect opportunity to explain what he is going to do to compensate the three million working families across the UK who will lose out as a result of his tax credit reforms."
George Osborne rebuffed critics of cuts to tax credits, insisting it was failure to control public spending that would be "economic cruelty" for working families.
He hit back after David Davis joined senior backbench demands for a rethink, warning that the squeeze could prove as damaging to the party as the Poll Tax was under Margaret Thatcher.
Mr Osborne said a "typical" family with one person working full-time on the national minimum wage will be better off overall, when all of the government's changes to benefits, income tax allowances and the establishment of a new "national living wage" are taken into account.
And he told ITV's Good Morning Britain that maintaining tax credits at their current level would force the government to divert money away from priorities like health and education.