Several years ago the Ginsburg Court refused to hear a similar plea from the forces supporting Terri. Incredibly though this Souter Court affirms a national "right to abortion," it says that euthanasia is a matter for "the states." On this old Anthony Kennedy Court, it's ultimately whatever Sandra Day O'Connor says, but preferably if it is in line with John Paul Stevens' Chicago school of liberalism or Stephen Breyer's Boston style of socialism.
If it isn't their life hanging in the balance, judges at any level would rather choose death, wouldn't they, (even though the most vulnerable should have the best protections).