But Cameron is facing rebellion from the unelected House of Lords and some of his own Conservative lawmakers over cuts to tax credits for parents and people in low-income jobs.
The House of Lords, Parliament's unelected upper chamber, is scheduled to vote Monday on whether to take the rare step of defying the House of Commons by striking down the cuts.
The Labour opposition is calling for a U-turn, and some Conservative lawmakers also oppose the move, which they say undermines the center-right party's claim to champion working people.
The government says the cuts will be offset by other measures, including a higher minimum wage.
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The House of Commons has already approved the cuts.
Members of the Lords will debate them Monday and are due to vote on amendments rejecting or delaying the proposals.
By tradition the House of Lords can only revise, and not overturn, legislation passed by the Commons. But the tax-credit changes take the form of new regulations rather than a new law, so members of the Lords say they have the power to stop them.
"These are people who go to work, look after their kids, do everything asked of them and they are going to lose, on average, about 1,300 pounds a year," he said.
Cameron insisted this week that the cuts were necessary. But Education Secretary Nicky Morgan said Treasury chief George Osborne was "in listening mode" and could take steps to lessen their impact.
"People are of course going to be worried," she told the BBC. "But I think it's a question of working through all the numbers. ... What is the alternative? We have to get the economy straight.