Some 87% of adults think the system is "facing severe problems", rising to 94% among the over-55s, research commissioned by Christian think tank Theos found.
The majority, 68%, believe claimants should only benefit from state services if they have paid into the system, even if they are in real need, and the same amount said welfare should be a "safety net for only the poorest and neediest", according to the ComRes poll.
But half the population believe the wealthy should be able to receive benefits if they have paid taxes.
The findings comes as Prime Minister David Cameron was moved to defended the Government's welfare reforms in the face of criticism from the head of the Roman Catholic Church in England and Wales.
Nearly six in ten voters believe pensions, the National Health Service, tax credits, child benefit, disability living allowance and unemployment benefit, will be cut or have virtually disappeared over the next three decades, the poll found.
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