In London, the 37 clerics on Wednesday were weighing the decision of US Anglicans, known as Episcopalians, to defy church policy and appoint the first openly practising homosexual bishop in the 70-million-strong worldwide Anglican communion.
They might decide to punish the Americans by declaring them "outside the communion" - a drastic move which could herald the end of an ancient alliance of 38 churches spread over 160 countries from Africa to Australia.
But after seven hours of talks, Irish Anglican leader Robert Eames emerged from London's 12th-century Lambeth Palace and suggested a more conciliatory solution was on the cards.
"It's moving towards a consensus situation," he told reporters. "Now, what form that consensus will be won't become obvious - if it is to become obvious - until tomorrow."
"There is a tremendous anxiety to maintain the Anglican community," he added. "I am optimistic that the Anglican communion will emerge from this stronger than it has ever been."
Eames said Wednesday's talks had given churchmen a chance to express their individual concerns about homosexuality - "concerns which are varied (and) which in some cases are totally coloured by the culture of that country".
"I am optimistic that the Anglican communion will emerge from this stronger than it has ever been"
Irish Anglican leader
Even one of Anglicanism's leading conservatives, American Anglican Council (AAC) President David Anderson, said there was only "a 20-35% possibility of a split" in the communion.
The clerics could decide to set the Americans a deadline to comply with the church's current position on homosexuality, or might simply decide to reflect further on the issue.
But if they fail to take firm action against the rebel Episcopalians, there is a risk conservative Anglicans - notably in Africa and South America - will leave the communion of their own accord.
The two-day meeting in London brings together 37 of the 38 leaders of the provinces of the Anglican church. The 38th, from the Philippines, was unable to attend.
The man with the unenviable task of bringing them to a common position is Anglicanism's spiritual leader, Archbishop of Canterbury Rowan Williams.
The crisis, the worst the Anglican church has faced for generations, was sparked by the decision in the US to appoint Gene Robinson, a divorced father of two and a practising homosexual, as a bishop.