The Labour leader told the Prime Minister to "wake up to reality" and "lead or leave" amid dissent from Tory backbenchers during the heated PMQs exchange.
To cheers from the Labour benches, Tory MP for South Cambridgeshire Heidi Allen expressed concerns over the welfare programme, adding there were "many of us" on the government's benches who believe changes were needed.
The PM sheepishly agreed to have a meeting with Ms Allen over the new benefit system, which rolls six means-tested working-age benefits into one payment.
Universal credit has been mired by delays, with vulnerable claimants forced to wait weeks for payments, throwing them into debt and threatening a spike in evictions.
Other claimants have complained about the complexity of the new system, which is made more difficult to manage without internet access.
Mr Corbyn repeatedly criticised the process in the chamber, quoting the Citizen's Advice Bureau in describing it as “a disaster waiting to happen.” He also called on Ms May to "show some humanity" by making the universal credit helpline free, when it currently costs callers up to 55p a minute.
He said: "Not only are people being driven into poverty but, absurdly, the universal credit helpline costs claimants 55p a minute for the privilege of trying to get someone to help them claim what they believe they're entitled to.
Ms May sat stony-faced as Mr Corbyn pointed out that "universal credit is only one of a string of failures of this government. Can't the Prime Minister […] wake up to reality and halt this process?"
"Everywhere you look it's a government in chaos. On the most important issues facing this country it's a shambles.
"Brexit negotiations - made no progress. Bombardier and other workers facing redundancy. Most working people worse off. Young people pushed into record levels of debt. A million elderly people not getting essential care. Our NHS at breaking point.
"This government is more interested in fighting among themselves than in solving these problems."
After Tory and Labour MPs heckled each other, Mr Corbyn added: "Isn't it the case that if a Prime Minister can't lead she should leave?"
The Department for Work and Pensions (DWP) said helpline calls cost up to 9p from a landline and between 3p to 55p from a mobile, which is dependent on a person's mobile package.
Speaking outside the Commons, the PM's official spokesman said: "As I understand it, most of the issues can be resolved online but if there are issues where people want to call the hotline and are concerned about the cost, DWP will call them back."