If not, Gordon Brown said he will revisit the idea of presumed consent in England.
Ministers tabled the Human Transplantation (Wales) Bill in December 2012 to introduce presumed consent in organ donation.
Both Barry and Elizabeth are passionately in favour of organ donation but just as strongly opposed to presumed consent.
Mr Jenkins said presumed consent would damage the delicate relationship between the donor, the donor's family and the doctor.
No part of the UK has introduced a system of presumed consent yet, although Wales has said it intends to.
Health Minister Edwina Hart also attended the committee to provide an update on the presumed consent consultation for organ donation.
The taskforce has run focus groups to explore some of the complex issues around presumed consent before writing its report.
For some, of course, the concept of presumed consent is all wrong.
So in the light of his optimism where does that leave the next report from the Taskforce on the controversial issue of presumed consent?
The charity CARE argues that presumed consent isn't just misguided.
Presumed consent would mean that Welsh residents would be presumed to be organ donors unless they have joined an opt out register or immediate relatives object.
There was a warning too that when it comes to organ donation, the key is our understanding of what is about to change, of what 'presumed consent' means.
Indeed, the more Britain's task-force examined evidence from around the world, the more multifaceted the problem and the less obvious the benefit of presumed consent appeared to be.
However, Welsh Health minister Edwina Hart, has rejected the all-party Welsh Assembly report when they decided against presumed consent after weeks of evidence and is still pressing ahead.
Archbishop of Wales Barry Morgan is opposed to presumed consent.
Wales has consulted on a change to presumed consent organ donation which means that, as in Spain, people would have to opt-out from the register, rather than opting in.
Alison John, an ambassador for Kidney Wales Foundation, who has had three transplants with four organs, said she believed having a presumed consent system is the "only way forward".
The British Medical Association has been campaigning for presumed consent - where all people are assumed to be willing to donate organs unless they opt out - since 1999.
It places Wales above many other European countries, including France (23.8 pmp), Italy (21.6 pmp) and Belgium (20.5pmp), which already has a system of presumed consent, according to figures for 2010.
The government has proposed switching to a system of "presumed consent" for donation after death - meaning everyone would be regarded as a potential donor unless they had specifically opted out.
Mrs Hart said that the consultation has shown that there is "a public aptitude" for presumed consent, and that she will seek a Legislative Competence Order for "soft opt-out" on presumed consent.
Spain has a "presumed consent" law, where individuals are automatically considered an organ donor unless they opt out, but Watson said that is not the only factor that explains the country's high level of organ donation.
But KWF used the example of Belgium, where only 2% of the population opted-out of a presumed consent system and said it proved a "great success" with donor rates increasing by 55% in the first five years.
Not only might a shift to presumed consent damage the vital relationship of trust between dying patients and their doctors, the task-force says, but it could also remove the emotional benefit to recipients and their families of knowing that the organs had been freely surrendered as a gift.
So, argues the Welsh Government, add 15 to that number - the expected rise in the number of donors under presumed consent - 15 people, 45 organs and that is not an insignificant number of lives saved, or money saved. 15 might not sound very much but purely in terms of cost to the NHS, just one single donor, argues the government, would make this policy worthwhile in cost terms.
"Evidence that any system of 'automatic' donation increases the supply of organs - whether it's called 'presumed' consent, 'deemed' consent, or 'opt-out' - is still disputable, " added the bishops.
While it is technically an opt-out system - where consent is presumed - in practice it operates on more of an opt-in model, where consent is sought from the family of the deceased person.
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