Yes, I've noticed that "unappeasable" is the cute slang-of-choice for those who defend the Administration's do-nothing policy on border control.
You're 'unappeasable' by expecting the law to be enforced- at least in the eyes of those who intend to do nothing, and expect you to put up with it.
Funny how the unappeasables are going berzerk right when Bush puts two very Conservative Justices on the bench.