A committee of MPs has warned the limit has unintended consequences no government should be willing to accept.
The Work and Pensions Select Committee said the Government's justifications for the policy were based on assumptions that "simply do not hold true" and a "crude and unrealistic" distinction.
The committee published its final report of the current Parliament on Sunday, which concluded the Government must lift the two-child limit and return to providing support for all children through the benefits system.
The report said the limit will leave families having to stretch "frozen and capped" incomes to breaking point and children could bear the brunt of its impact.
It added: "The Government argues that the two-child limit will not increase child poverty because it will encourage families to increase their incomes from work.
"That may be possible for some. But for many, especially lone parents, the difficulty of accessing affordable childcare means that working more hours simply isn't an option.
"Those families are left with no choice but to make their already frozen and capped incomes stretch ever further - sometimes to breaking point.
"All too often it will be children themselves who bear the impact."
The report also said the Government had not provided any evidence to dispute experts forecasting that the policy will "significantly increase" child poverty.
It said it did not recommend scrapping a major policy lightly, but added: "On the evidence, the two-child limit not only fails to achieve the Government's own objectives but has unintended consequences that no government should be willing to accept."
The committee said the Government's arguments assumed all pregnancies were planned and in full knowledge of its benefits policy, when these "simply do not hold true".
The distinction between families on benefits and those who are working was "crude and unrealistic" because anyone in work could lose their job, fall ill, be disabled, or be bereaved tomorrow, it added.
The committee said that by the Government's logic, only the "wealthy few with the financial resilience to withstand all of life's misfortunes without recourse to the benefits system" could ever responsibly decide to have more than two children.
Rt Rev Paul Butler, Bishop of Durham said he hopes the new government would accept its findings.
He added: "The two-child limit takes support from families when they need it most, locking children in poverty during the most crucial years of their lives.
"I hope that not only the Department for Work and Pensions, but also the Treasury will accept the recommendation of this report and that a new government will act swiftly to reverse this policy and ensure all children thrive."
The committee's chair Christian MP Frank Field added: "Any family in this country, except the super-rich, could fall foul of the two-child limit if their circumstances changed for the worse.
"This is exactly why social security must act as a national insurance scheme covering people when they're most exposed to hardship - not increase it."
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