Speaking at the Conservative Party Conference on Wednesday, Miller responded to the Gordon Brown's announcement last week promising to provide 10 hours of free childcare a week for 250,000 two-year olds from families "on modest or middle incomes" within five years.
The Government intends to pay for these plans by scrapping existing tax relief on childcare, which currently can save basic rate taxpayers as much as £962 a year, rising to £1,195 for top-rate taxpayers.
Miller said: " It is hard sustaining family life... The prime minister is axing [tax efficiencies on] childcare that 300,000 working parents need.
"These are basic rate taxpayers, working in areas such as the health sector and doing vital jobs. They rely on this support.
"Hard-working families will be left to pick up the pieces and this has got to stop."
A Conservative Government will support families, building systems around them for childcare."
Marc Woolfson, account director at Westminster Advisers, told HR magazine 340,000 parents and 35,000 employers currently use tax-efficient childcare vouchers and a report earlier this year from the Department of Children Schools and Families found such vouchers were ‘very popular' with parents and employers.