Leading charities have written to every MP urging them to support the controversial embryo research bill, the BBC has learned.
Hybrids are made using an animal egg mixed with human genes
Cancer Research and the British Heart Foundation are among more than 200 charities in favour of the creation of human-animal hybrids for research.
The prime minister is facing dissent over the bill, from some of his Labour MPs and leading Catholic clergy.
But Health Secretary Alan Johnson said an "accommodation" would be found.
The letter, written by the Association of Medical Research Charities, says although there are ethical issues in allowing scientists to create embryos that combine human DNA and animal cells for research, the move offers "considerable benefits" to future patients.
The letter goes on to say the charities believe there is considerable public support for the move.
The letter states: "... public understanding of the importance of the use of early-stage embryos and ensuing stem cell research remains robust; there is a real acknowledgement of its potential for those who are ill."
Mr Johnson has said an "accommodation" will be reached for those Labour MPs who are opposed to parts of the Human Fertilisation and Embryology Bill.
Prominent Catholic clergy have called for all MPs to have a free vote - Conservative leader David Cameron and Liberal Democrat leader Nick Clegg will allow their MPs a free vote.
It is understood Labour MPs may be allowed to abstain on parts of the bill, as long as its passage is not threatened.
Alan Johnson told Sky News: "I believe... once we have discussed all these issues and seen all the safeguards in the bill, that there will not be a split.
"But there will be an accommodation for those who have a particular sensitivity around this, including those whose sensitivity relates to their faith."
Cardinal Cormac Murphy-O'Connor, the Roman Catholic leader in England and Wales, said MPs would want to vote on the Human Fertilisation and Embryology Bill according to their convictions.
"Certainly, there are some aspects of this bill on which I believe there ought to be a free vote, because Catholics and others will want to vote according to their conscience," he told Sky News in an interview broadcast on Sunday.
"I don't think it should be subject to the party whip."
The government says the medical benefits of allowing the creation of hybrid embryos for research purposes could ease the suffering of millions of people.
The embryos are made by combining animal eggs with human nuclei, which can then be grown into stem cells and used by scientists. The bill comes in response to a shortage of available human eggs for research.
Mr Johnson said the bill tackles deadly and debilitating diseases.
"For people out there suffering from Parkinson's disease and motor neurone disease, this is not a question of some issue about the procedure through the House of Commons," he told BBC News 24.
"This is an issue about whether we can find the drugs that can cure their illnesses. So this is the heart of the matter."
One Catholic Labour MP, Joe Benton, has warned that a "substantial number" of fellow Labour MPs are ready to defy the government if there is no free vote.
Welsh Secretary Paul Murphy is reportedly prepared to quit the cabinet rather than vote for the bill. Other Catholics in the cabinet are Transport Secretary Ruth Kelly and Defence Secretary Des Browne.
Northern Ireland Secretary Shaun Woodward said the bill was an important piece of government business which must be passed, but suggested a compromise was possible.
He told Sky News: "I believe it is possible, if we listen to the arguments and we remove the misunderstandings, to find a way forward so the government can complete its business."
But in an interview with the Sunday Telegraph, Labour MP Stephen Byers - a former cabinet minister under Tony Blair - said the public would "look on in disbelief" if Mr Brown did not offer a free vote.
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Other senior Catholic clergymen including Scottish leader Cardinal Keith O'Brien and the Archbishop of Cardiff, Peter Smith, have also called on Mr Brown to allow a free vote.
And on Sunday the Anglican Bishop of Durham issued a rallying call to all faiths to object to the "1984-style" proposals.
The Right Reverend Tom Wright accused ministers of pushing through legislation from "a militantly atheist and secularist lobby".
Liberal Democrat Evan Harris, a member of the Commons Innovation, Universities, Science and Skills Select Committee, said it was right to conduct research that "might be used to treat people with terrible diseases".
The bill received its first reading in the House of Commons in February, and while no date has been set for its second reading - or approval in principle - it is viewed as a key piece of legislation on the government's agenda.
The bill is designed to bring the 1990 regulatory framework for fertility treatment and embryo research in line with scientific advances.