The Building Societies (Distributions) Bill by Douglas French MP, was backed after he told the House of Commons that it was wrong to stop handicapped people from getting a share of the handouts.
They include second signatories to accounts where the first-named are trustees on the member's behalf. Many nursing homes have one trustee account on behalf of several members at once.
Mr French said last night: "I received a lot of sympathy and support from both sides of the House. The second reading will be on 14 February.
"That might be a bit more difficult because there are other items of business on the agenda for that day. I am in the hands of others ahead of me."
Support for his measure also came from Treasury ministers, who are also trying to obtain Parliamentary time for a separate Building Societies Bill.
Mr French estimates there may be at least 100,000 members of those societies seeking an immediate stock market flotation, including Halifax, Alliance & Leicester, Woolwich and Northern Rock, who would benefit from his measure, at a cost of about pounds 10m-pounds 15m. Several times this number may be affected if other societies decide to float.
"This is considerably less than the amount that societies have paid to City institutions," Mr French said. "One wonders why these same highly paid City institutions were not able to find a formula to allow such payments to handicapped society members."
Mr French's Bill comes as societies face hundreds of thousands of calls from members who fear they may be denied a share in the flotations.
Halifax Building Society yesterday said that staff working on its telephone hotline were handling up to 30,000 calls a day. Most are straightforward.
But a Halifax spokeswoman said: "We have said before that with 8.5 million members it would be unlikely if we did not make mistakes. Just 0.5 per cent of mistakes would be enough to fill Wembley Arena."
Among those left in the cold are two teenage brothers with similar-sized Halifax accounts, whose mother contacted The Independent.
One, aged 18, will receive a basic share entitlement worth about pounds 900. The other, who is 16 and under-age, will receive a cash payment worth only pounds 10. "You can imagine that one is rather pleased while the other is bitterly upset," their mother said.
Also furious with the society are Ian and Marjorie Strang, a couple who have been Halifax borrowers and savers for more than 10 years. They hope for a double handout worth at least pounds 1,600.
However, Halifax deducted the couple's mortgage payments from Mrs Strang's account on 31 December instead of the normal date of the first of each month, reducing her balance below the pounds 100 needed to qualify for free shares.
Gary Marsh, Halifax head of corporate affairs, said it would be wrong to comment on Mr French's Bill while members were still voting on the existing proposals.