The Australian Museum in Sydney has taken on that role, as a body devoted to both good science and public communication. The Myer Foundation has helped fund the initiative. So far, the proposal has not received any government funding. As a council member of the consumers' association, I have supported the idea of the consensus conference. But I can see why governments would be wary of the proposal.
Most governments prefer to put money into activities, which are under their control.
Consensus conferences overseas have typically led to consumers being better informed and less fearful, but that cannot be guaranteed. There are certainly irrational fears about genetic manipulation. But I think those fears are more likely to be dispelled by an open process in which a representative group is able to interrogate the experts. The community seems to be increasingly reluctant to take the views of scientific experts on trust, especially if they are on the payroll of a government or industry body. The considered verdict of a lay panel should have more public credibility.