Four Liberal Democrat MPs have expressed their unease about the budget by demanding a vote tomorrow night on a proposal for the Treasury to investigate the impact of the VAT increase on poor families.

They have tabled an amendment to the budget resolutions saying that the Treasury should carry out an assessment of the impact of the new 20% VAT rate "on business, charities and households across the income and age groups" and that the findings should be reported to parliament.

The amendment is not likely to be put to the vote.

But that fact that it is on the order paper shows some Lib Dem MPs are not convinced by the claims that have been made about the budget being progressive.

Andrew George, the St Ives MP who tabled the amendment, said that he hoped that Danny Alexander, the chief secretary to the Treasury, would agree to commission a report on the impact of the budget.

Government sources have indicated that this is unlikely, but the Lib Dem backbenchers will get another chance to raise the issue when MPs debate the finance bill later in this session of parliament.

The budget is seen as the first test of the strength of the coalition between the Lib Dems and the Tories and ministers were alarmed last week when Simon Hughes, the deputy leader of the Lib Dems, suggested that the Lib Dems would amend the finance bill to make it fairer. He subsequently retracted his comment.

But Bob Russell, the Lib Dem MP for Colchester and one of the four MPs who has signed the George amendment, yesterday refused to rule out voting against the government on this issue.

"I'm not ruling anything in or anything out," said Russell, who has been the Lib Dem MP most critical of the budget.

"The only thing that I'm ruling in is a desire to eliminate child poverty in the UK."

George Osborne, the chancellor, insisted last week that his budget was progressive, and that the rich would pay more proportionally.

But the Institute for Fiscal Studies and others have said that, when you take out the impact of measures already proposed by Labour and when you include the impact of public spending cuts, the poor will be hit the most.

Today two opinion polls – YouGov for the Sunday Times and ICM for the Sunday Telegraph – put the Lib Dems on just 16%, compared to the 23% they got at the general election.

Their support seems to have gone down since the budget, suggesting that coalition's decision to raise VAT may have damaged the party that campaigned aggressively against a VAT increase at the election.