Parents should only be able to claim child benefit for four children under a think tank's plans to trim £1 billion from the welfare bill.
The plan put forward by the right-of-centre Policy Exchange would see payments reduced for each child after the first, with no child benefit at all for fifth and subsequent children born after April 2016.
An opinion poll commissioned by the think tank found that more than two thirds of people would support capping child benefit at four children.
For households with no one earning more than £50,000 child benefit is paid at £20.50 a week for the oldest child, and £13.55 for any additional children.
Unless there is a change in policy the think tank forecast those rates would increase to £22.40 and £14.85 in 2019/20.
But under the Policy Exchange plans, child benefit rates would continue to rise until the end of the next parliament at a rate of 1% for the first and third child of a household and by 2% for the second child.
The weekly payment for a fourth child would remain at the 2015/16 level of £13.70 and the benefit would be scrapped altogether for fifth and subsequent children born after April 2016.
This would mean that in 2019/20 the weekly rate would be £21.50 for the first child, £14.85 for the second, £14.30 for the third and £13.70 for the fourth.
The plan is based on research which suggests that the arrival of the first child has the largest impact on family finances but with each additional child the marginal cost falls.
The proposed changes to child benefit, which could save £1 billion over the course of the next parliament, are contained in a forthcoming Policy Exchange report on the welfare system, which is aimed at showing how savings could be made between 2015 and 2020.
George Osborne has indicated that he wants to cut £12 billion a year off the welfare bill.
A YouGov poll for Policy Exchange found 67% thought that people who have four children should not receive extra child benefit if they had a fifth, with 20% saying they should and 13% unsure.
The Policy Exchange report's author Steve Hughes said: "The Chancellor has suggested that annual welfare savings of £12 billion will have to be found to avoid further and faster cuts to departmental budgets.
"Choosing where this money comes from is not easy, but with such high levels of public support, capping child benefit at four children and re-designing payment levels offers a very real opportunity to generate some much needed savings in the fairest way possible."
:: YouGov surveyed 2,095 British adults online on July 3-4. Data were weighted to be representative of all British adults.
Deputy Prime Minister Nick Clegg told LBC radio: "I think you should always look at the benefit system and there will need to be further reforms of the benefit system.
"In the past the Conservatives said it shouldn't be more than two children, now there's a report that says four. It keeps chopping and changing.
"I'm very happy to continue to look at these things. I just don't like the whiff of Chinese-style policy that says the state will give you support for one child but not two children or whatever numbers are coming up.
"You need to ask the Conservatives what their policies are and we will come up with our own in the months to come for our own manifesto as well."