The government faces a rebellion over embryo laws unless Gordon Brown allows a free vote, a Labour MP has warned.
Gordon Brown is under pressure from his own MPs.
Joe Benton, who is Catholic, said a "substantial number" of fellow Labour MPs were ready to defy the government.
The leader of the Catholic Church in Scotland has urged Mr Brown to let MPs vote with their conscience on laws allowing human-animal embryo research.
Downing Street has said a decision on whether to allow a free vote will be taken "in due course".
The Human Fertilisation and Embryology Bill is designed to bring the 1990 regulatory framework for fertility treatment and embryo research in line with scientific advances.
Among its many clauses, the bill would allow scientists to create hybrid human-animal embryos for research.
In his sermon to be delivered on Easter Sunday, but released on Good Friday, Cardinal Keith O'Brien described the plans as "monstrous". He warned Mr Brown against imposing a three-line whip on Labour MPs - which orders them to vote with the party line.
His intervention came amid reports on BBC Radio 4's World at One that at least one member of the cabinet, Welsh Secretary Paul Murphy, is preparing to quit the Cabinet rather than back the bill.
The BBC's political correspondent Reeta Chakrabarti said Mr Murphy's spokesman responded to the report by saying there were "big scientific and conscience issues involved" and Mr Murphy's Catholic faith was very important to him.
Asked if Mr Murphy did intend to resign if there was no free vote, he referred to remarks made by Gordon Brown earlier this week in which he said everyone should have the right to exercise their conscience.
He said that ministers were "trying to find a way through it".
Other Catholics within the cabinet are Transport Secretary Ruth Kelly and Defence Secretary Des Browne.
If any of them defy a three-line whip, they would also be expected to resign.
Although he did not wish to name them, Mr Benton, who is MP for Bootle, said: "I know for a fact there would be ministers who would resign over this issue.
"I know there are people in Cabinet who will object on moral grounds. It's more than likely there will be more than one."
He added: "There would be a quite significant number of Labour Catholic MPs and members from other denominations and some of none who will oppose this motion."
Labour backbencher Geraldine Smith, also a Catholic, shares the cardinal's concerns about the bill and believes the issue is a matter of conscience.
"There are a number of government whips that share my views and members of the Cabinet," she told BBC's World at One.
"I would be very, very surprised if at the end of the day we did not end up with a free vote on this matter.
"With a whip or not, I will be voting with my conscience," she added.
But other MPs believe the government will stick to its guns. Labour MP Brian Iddon, who sits on the innovation, universities, science and skills committee, said he believed that while the government might offer some ministers and MPs the chance to abstain from elements of the bill, a free vote would not be allowed.
He said: "This is a key government bill. It was not given a free vote in the House of Lords.
HAVE YOUR SAY
I wonder how the cardinal would view it if one of his own family were to benefit from any future success in this field
James Rooney, Glasgow
"The best that can happen to those with religious consciences is that they might get a conscience vote. But people will not be allowed to vote against this bill, I'm told.
"We have lost ministers before on key government bills. People resigned over the invasion of Iraq."
On Wednesday, Conservative leader David Cameron called on Mr Brown to allow Labour MPs to have a free vote on the bill when it returns to the House of Commons later in the year.
Both the Conservative and Liberal Democrat leaders have allowed their MPs to have a free vote on the more controversial aspects of the Embryology Bill.