Leaked documents said the Employment and Support Allowance (ESA) was "one of the largest fiscal risks currently facing the Government", leaving it "vulnerable" to a breach in the cap for 2015/16.
Rachel Reeves, for Labour, said: "The Work Capability Assessment is in meltdown, there are huge backlogs for Personal Independence Payments, a Work Programme that's failing disabled people and the chaos of Universal Credit.
"It is a catalogue of total failure and threatens huge costs to the taxpayer.
"David Cameron must urgently get a grip of this chaotic department."
But the DWP said it was "outrageous" to suggest it was on track to breach the cap, which covers welfare payments excluding the state pension and some unemployment benefits.
If the total annual benefit spend comes in over the cap, ministers must go to the UK Parliament to explain and ask MPs to approve additional spending.
The leaked memos said the cost of ESA was projected to rise by nearly £13 billion by 2018/19, largely due to people moving on to the benefit from Jobseeker's Allowance.
A DWP spokesman said: "These are spurious scenarios and do not reflect our forecast of future spend provided at the Budget.
"It is outrageous to somehow link these to us potentially breaching the welfare cap."