I would think that there would be a small percentage, maybe more than 1% but not much more than 3% or so (just an estimate, nothing concrete though) of the population that would voluntarily opt out. Ironically, I would think that if euthanasia was legal and very accessible for anyone that wants it (almost no strings attached, only being of legal age and after maybe a short waiting period, such as 6 months to 1 year at most (barring terminal illness), and consent from the individual), there may even be people who may stick around just a bit longer since they know they can opt out at any given time for any reason.
As for the moral panic and those who fear slippery slopes and various other overblown concerns, again, I don't believe those would be warranted or grounded in reality. It will just mean more resources and less competition for the majority of people competing for resources and other things. Basically the people who want to stay will stay while the people who desperately want out will have their exit.