The prime minister and Chancellor Rishi Sunak have been resisting demands to set out new tax-and-spend measures to alleviate the squeeze.
Some Conservative backbenchers accept an emergency budget is required and Labour will challenge them to back its binding vote on Wednesday.
The Labour amendment to the Queen’s Speech will note that the government’s legislative agenda it contains “fails to bring forward immediately” an emergency budget.
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It will also urge ministers to set out a “new approach to the economy that will end twelve years of slow growth and high taxation” under the Tories.
Labour’s thinking was the amendment would not force ministers to bring forward a new Bill by a specific date if passed, but would put massive pressure on the government to draw up plans.
Opening the final day of the six-day Queen’s Speech debate, shadow chancellor Rachel Reeves will highlight the “unfair” tax system adding to the squeeze on wages.
“That’s why the Conservatives must back our motion today, not just for them to come forward with an emergency budget to tackle the cost-of-living crisis, but to set out the plan Britain deserves to get our economy firing on all cylinders,” she is expected to add.
The government’s programme will almost certainly pass, with the prime minister commanding a large majority in the Commons and the Queen’s Speech being seen as a vote of confidence, so voting against it could cause MPs to lose the Tory whip.
Despite apparent resistance to an emergency budget, Foreign Secretary Liz Truss said the chancellor is "looking at all options" when asked if one would be used.
On the cost of living more generally, she said: "We are looking at what more we can do to support those families who are struggling because we recognise it is a very difficult time."
Those who have put on record their support for an emergency budget could face questions over why they did not back the measure when they had the chance.
Mr Johnson has promised measures to help ease the pain of wages falling further behind soaring inflation, but was resisting caving in to demands for a fully-fledged budget.
On Tuesday, Labour failed in its bid to amend the Queen’s Speech to secure a windfall tax on the soaring profits of oil and gas companies to help provide relief to the public.
Conservative former minister Robert Halfon and Mel Stride, the Tory chairman of the Treasury Committee, both indicated support for the policy, with the former labelling oil company bosses “the new oligarchs”.
But the amendment was rejected in the House of Commons by 310 votes to 248, majority 62.