Philip Hammond is facing questions from Labour on his Budget stamp duty cut for first-time buyers and from Tory Eurosceptics on proposed payments to Brussels after Brexit.
Labour MPs are challenging the Chancellor over claims by the Government's own Budget watchdog, the Office of Budget Responsibility (OBR), that the stamp duty cut will push up house prices.
Some Labour backbenchers have also dismissed the stamp duty cut as a "gimmick" which will help young professionals in London but do nothing for people in areas where property prices are low.
Meanwhile, Eurosceptic Conservative MPs are demanding answers from Mr Hammond about OBR forecasts suggesting the UK will pay the European Union £3.5bn in the year after Brexit.
The Chancellor will be challenged on these and other issues - such as his failure to lift the public sector pay cap - in a round of post-Budget breakfast TV and radio interviews.
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Later, shadow chancellor John McDonnell will launch Labour's fightback when he opens day two of the four-day Budget debate in the Commons, when pro-Brexit Tories will query the Brussels cash.
Mr Hammond was cheered loudly in the Commons by Tory MPs - and again when he addressed them at a meeting of the backbench 1922 Committee - for his stamp duty cut.
He is abolishing stamp duty altogether for first-time buyer purchases up to £300,000, and on the first £300,000 of the purchase price of properties worth up to £500,000.
In his initial response to the Budget, Jeremy Corbyn told MPs (BSE: MPSLTD.BO - news) : "We back the abolition of stamp duty for first-time buyers because it was another Labour policy at the election, not a Tory one."
But then the OBR said in its 258-page Budget breakdown: "First (Other OTC: FSTC - news) -time buyers purchasing a property over £500,000 will not be eligible for this relief, and will therefore face the same marginal stamp duty rates on the first £500,000 as before."
And in a prediction that was seized on by Labour MPs, the OBR said: "We expect this to increase house prices by 0.3%."
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Former shadow cabinet member Rachel Reeves, who chairs the all-party Business Select Committee, told MPs the housing measures in the Budget were "the exact opposite from what we need if we want to ensure that more young people and more families can get on the housing ladder".
John Mann, who chairs the Treasury sub-committee, said the average house price in his Bassetlaw constituency in Nottinghamshire was about £135,000 - just above the £125,000 threshold for stamp duty payments.
He added: "Few first-time buyers have the means to afford properties costing up to £300,000.
"Very few first-time buyers at all are buying properties costing that much in the North.
"I'm sure this little boost will help young professionals in London, but for those working hard in ordinary jobs in my area it doesn't address the root cause of problems for first-time buyers.
"More affordable homes and decent, stable jobs to allow people to save for them are the way to tackle the housing crisis.
"Today's announcement on stamp duty is little more than a gimmick."
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The challenge to the Chancellor over post-Brexit cash payments to Brussels was raised in the Commons Budget debate by the Eurosceptic Conservative MP Jacob Rees-Mogg.
He said he suspected Treasury forecasts suggesting Britain would pay the EU £3.5bn in a year following Brexit must be an error.
Mr Rees-Mogg told MPs he had spotted figures in Budget documents outlining an "own resources contribution" to the EU in 2022/23.
"This is rather like spotting an error in Wisden Cricketers' Almanack, something that is very rare to do and indicates an occasional failing that I hope will be put right and we will discover that this is not intended," he said.
"Because if it is, it means we won't in fact be stopping our contributions to the European Union, and that would be very strange.
"And to have them described as own resources is even more peculiar, because that assumes we are still members, so I think there is an error there."
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Mr Hammond's deputy, Treasury chief secretary Liz Truss, told Mr Rees-Mogg: "Those forecasts are made by the OBR.
"The OBR were provided with the Prime Minister's Florence speech, the basis on which we are negotiating with the EU. It is up to them to make their own independent forecasts."