With nursing as one example, what other jobs are safe from outsourcing?

Any government job

I would think teaching would be a safe job. There will always be either children or university students.
Funeral directors, morticians, etc. People are always going to be dying.
Are you sure about Nursing. Plans are afoot to outsource in many NHS Trusts.

Safer jobs are.............RODENT OPERATIVE.................VERT... CHALLENGED ROBOTS........CANINE WALKERS...............SPERM DONORS.
Those of the elected officials who are the driving force behind this. BOTH PARTIES. Law enforcement, fire fighters, garbage collectors, nurse aides, those in the importation business and prostitution. Of course many of those positions will be filled by illegal immigrants. Expect that to increase now when the Democratic Congress allies with the Administration too push the amnesty program through and to expand immigration in general from Mexico. So even the 'safe' jobs will face another form of outsourcing from within our borders.
I'm not certain there are any jobs safe from outsourcing. For example, the portion of a nurse's job that revolve around patient record keeping can be outsourced to countries where transcription is cheaper and through technology which removes the need for a nurse to keep track of a patient's paper chart.

Teaching can certainly be outsourced given technology. Why can't a two-way video conference with a teacher/lecturer and students able to interrupt and ask questions have the teacher thousands of miles away?