I do think that many would still reject the switch, but I think people who believe in reason would understand if the decision was logical (as far as discovering the truth... not the same as discovering a constituency disagrees and one might not be re-elected).

I'm trying to think of historical leader (business or political) who have done this, but nothing comes to mind. If someone pops up, I'll drop you another reply. I know there are a few business leaders who have done something of this sort, but they're just not making themselves available for me right now!