Proposals to give the public shares in part-nationalised banks RBS and Lloyds have been backed by Nick Clegg.
The idea is that individual taxpayers would benefit from any long-term gains when shares in the banks are sold.
The deputy prime minister said it was important British people were not overlooked after their money was used to keep the banking system alive.
The Treasury said all options would be considered but Labour dismissed it as a headline-grabbing exercise.
Under the plan, the 45 million people on the electoral roll would be given free shares in the bailed-out banks, Royal Bank of Scotland and Lloyds Banking Group.
The shares would only have any value above a "floor price", equivalent to what the government paid for the holdings, so the Treasury could cover the cost of its investment.
That price is estimated at 74p per share for Lloyds and 51p for RBS.
The idea for so-called people's shareholdings, first suggested in March, was developed by City firm Portman Capital with the support of the Lib Dems' Treasury Parliamentary Committee, chaired by backbencher Lib Dem Stephen Williams.
He argued that the mass distribution of the bank shares would be the fairest way of giving taxpayers a share of the rewards, of getting back the money the government paid out in 2008, and would help restore confidence in state-owned financial institutions.
Mr Clegg has written to Chancellor George Osborne in support of the proposal.
Speaking on a trip to Brazil, Mr Clegg said: "Psychologically it is immensely important that the British people feel they have not just been overlooked and ignored.
"Their money has been used to the tune of billions to keep the British banking system on a life-support machine and they have absolutely no say at all in what happens when normality is restored.
"I think, in a sense, as a society we are condemned to take an interest in our banking system."
He said the scheme would give the Treasury an assurance that they would "break even" without allowing it "the freedom to grab the windfall if there is one".
Business Secretary Vince Cable said proposals were at a "preliminary" stage and it would be some years before the banks were in a position to be returned to the private sector.
But he said it would be a way for tax-payers to benefit after "saving" the banks.
Mr Cable, who has previously accused the banks of privatising their profits and socialising the losses, said the proposal would be one way of reversing that he said.
There have been suggestions the scheme could cost hundreds of millions to administer but Mr Williams, the MP who floated the idea, told the BBC he was convinced it would be cheaper than a conventional privatisation - which would see the Treasury charged "huge fees".
He added that people with "surplus cash" would be able to buy shares, but millions of citizens would miss out, despite having "felt the pain of contributing" to the bank bailout in the first place.
The idea has also been backed by the Conservative backbencher John Redwood, who told the BBC: "It is a great opportunity so that the taxpayers can be involved, the taxpayers could then it discipline the banks as their owners and shareholders and they can get something back when the banks have sorted themselves out."
The Tory right winger asked Chancellor George Osborne about the idea in the Commons earlier in the week.
Mr Osborne told him was "always happy to discuss ideas" about disposing of the bank shares and the "good bank" in Northern Rock was going up for sale.
But he added: "We want to exit from our shareholdings in RBS and Lloyds in due course, but we do not judge now to be the right time."
Ahead of last year's general election, Mr Osborne himself floated the idea of a "people's bonus plan", under which the public would have been offered discounted shares in state-owned banks.
The taxpayer owns 83% of RBS and 41% of Lloyds after the government invested about £65.8bn in 2008 at the height of the banking crisis.
A Treasury spokesman said: "While the question hasn't arisen at the moment, we've said we shall look at all options".
Labour dismissed the proposal as a headline-grabbing exercise by Mr Clegg that had not been properly thought through.
Shadow chancellor Ed Balls said: "The test for what happens to the nationalised banks must be the long-term best interests of the taxpayer not the short-term need to get headlines for Nick Clegg's overseas trip.
"The government needs to urgently explain what impact this proposal will have on the public finances, what the administration costs are estimated to be, how the scheme would work and what effect it would have on the balance sheets of the banks."