They know that nothing less than the long-term survival of the Irish Catholic Church is at stake because of their collective failure to address the cancer of child sex abuse by members of the clergy over the past decades.
If they fail to address this issue once and for all and come completely clean on the extent of it and the steps they are taking, they will find themselves in a tightening death spiral when they arrive back in Ireland.
Irish people will no longer accept for a second that a Roman collar gives a man the right to carry out arguably the worst form of crime short of murder -- that of child sex abuse. If the Church was a major corporation with a history of covering up child abuse by its workers, it would have been shut down long ago.
Put simply, there is little confidence in the present leaders of the Irish Church because of what has been allowed to happen on their watch. Following the Famine, the Church became an almighty institution with a top down leadership that brooked no argument, even from elected political leaders.
When the cancer of child sex abuse by clergy began to spread, they immediately went into denial mode, and for many years succeeded in brushing the worst of the issue under the rug.
Now that time has passed, the Church faces the bleak landscape of a population that is deserting them in droves and young people who have become overwhelmingly cynical about men of the cloth.
It will be an extraordinary moment when Pope Benedict addresses the issue with the bishops. When was the last time that a Pope spent so much time on a corner of his Church that has always been the ultimate team player? Not for nothing was the phrase, "Rome dictates and Ireland takes" invented.
Now, the Pope will no doubt seek to dictate future policy in Ireland. He is not really clear of this issue himself, having incredibly promoted the Boston Cardinal Bernard Law after he was revealed to have covered up blatant child sex abuse in his Archdiocese.
So the plan they come up with has to be clear and perfectly simple. Any future episode of child sex abuse must be immediately turned over to authorities for prosecution. Any current cases on their books, still not investigated, must be taken up immediately. Any present or future bishop who covers up such an incident is complicit in a crime, must be forced to resign and be prosecuted also.
The Irish Church has an opportunity, strange as it may sound, to show the way on this issue to the rest of the Church, by enacting such direct and straightforward doctrines that there can be no ambiguity whatever about them.
Only by admitting the scope of the problem, coming completely clean and accepting strict future governance on this issue can the Church begin to find its way again.
Such methods will not come easy to men who are used to dictating rather than accepting rules and regulations. But is it their only hope of becoming relevant again as spiritual pastors in the life of Ireland.
The Rome visit is a critical crossroad.