Miliband will throw down the challenge in a visit to Eastleigh ahead of the 28 February byelection, saying: "Here is a chance for Nick Clegg to prove he can keep at least one of his promises."
Miliband will say he will set up a vote through an opposition-led debate or amendments to the finance bill, the legislation that will implement the March budget.
The Treasury chief secretary, Danny Alexander, also pointed out that Labour had not specified what form its mansion tax might take, and its design was critical.
But Miliband's aides said the Lib Dems had been pressing for a mansion tax to be included in a coalition budget for two years, but they had been rebuffed by No 10.
"We are providing them with the chance to show they are not colluding with the Tories, and to put a mansion tax on the statute book," a Labour official said. "They will now have an opportunity to start to address their record of failure by voting in favour of a policy they claim to support – they will be judged on what they do and not what they say."
In a stump speech in Eastleigh Miliband will say: "It's time for Nick Clegg and the Liberal Democrats to be honest with the people of Eastleigh and show whose side they are on. They must answer the question: will they vote with Labour in advance of the budget to force David Cameron and George Osborne to act?
"Or will the Liberal Democrats do what they have done for the past two and a half years – prop up a Conservative government that is squeezing the middle harder and harder."
Miliband will add that with Labour support the Lib Dems can form a majority in the Commons.
He says the political challenge for the Lib Dems is vital, because if they turn down the opportunity to vote for the tax on the rich, it will be seen as another betrayal similar to the vote to increase tuition fees.
The strength of the Miliband assault on the Lib Demos is striking and suggests that he is willing to see the Conservatives take Eastleigh at the expense of the Lib Dems – a more likely outcome if the Labour vote is strong, and the anti-Tory tactical vote minimised.
The calculation among some Labour MPs is that it would be more destabilising for the coalition to see Clegg lose, as opposed to David Cameron.
Miliband regards Labour's performance in Eastleigh as important to show how much the party has recovered in the south.
Labour proposes to levy a mansion tax on homes worth more than £2m, and could raise £2bn.
Clegg has said his mansion tax would be at 1% on properties worth over £2m, paid on the value of that property above that level.
Miliband's aides also urged the Lib Dems to publish the work they must have commissioned in government to show how the mansion tax could be implemented.
Just 10 London boroughs would account for 60% of properties valued at more than £2m.
Nearly half the purchasers of £1m-plus properties are foreigners, and many of them are institutions.
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