"Oh wow I’m sure a letter to mums will suddenly make childcare affordable," one critic said.
Government is investigating but watchdog calls it "highly unlikely" true scale of tragedy is clear.
Claims that people moving to the new benefits system would not lose out were false, influential committee finds.
"Patients and claimants are suffering and continue to suffer as long as these letters are sent out."
Charities fear new one-stop process will lead to more people losing payments.
Labour's Tom Watson described the job listing as "grotesque".
Household benefits are capped at £20,000 outside London.
One wheelchair user was forced to sofa-surf for a year after missing one Jobcentre appointment.
System to speed up claims of those with just weeks to live “has been removed”, charity says. DWP denies claim.
Demands for government to halt programme as its own data shows 'worryingly high' numbers drop off social security system