The drone strikes are unpopular with liberals. I am certainly ambivalent. So it is Obama's base that questions these strikes whatever support arises from the right. So don't take your appraisal as representative of those who usually support Obama, HIS base.
Even a superstitious man has certain inalienable rights. He has a right to harbor and indulge his imbecilities as long as he pleases. . . He has a right to argue for them as eloquently as he can, in season and out of season. He has a right to teach them to his children. But certainly he has no right to be protected against the free criticism of those who do not hold them. He has no right to demand that they be treated as sacred. He has no right to preach them without challenge." -H.L. Mencken