Don't construction jobs require licensed and bonded labor? They certainly do here in Alberta.
The mortgage problem certainly is not the result of illegal immigrants buying houses, this is a fabrication.

Most shortages in the health care industry are the result of inadequate funding, lack of funding for medical education, and poor wages for medical personnel.
This complaint by a Boston area medical student is typical-
Yearly tuition at Boston Univ. School Medicine- $42734, Fees $2914, Room and board $11933, Books and supplies, $2843. Only about 30% of students obtain any grant aid. Debt after graduation astronomical!

In California, some eight million people live in officially designated primary care shortage areas. An a letter to the NY Times, Carla Kakutani, President of the California Academy of Family Physicians writes:
"In California, nearly eight million people live in officially designated primary care shortage areas. Millions more seriously ill patients must wait several weeks for appointments or seek care in emergency rooms, which drives up health care costs and leaves patients without essential follow-up care.
Family physicians in California support universal coverage and comprehensive health care reform that addresses the primary care doctor shortage. Ignoring this problem would derail any attempt to provide universal health care."
And more to the letter, but that is enough. No blame is attached to illegal immigrants. NY Times, April 13, 2008.

Are conditions any better here in Canada? Not in wealthy Alberta, home of the tar sands and supplier of much of the petroleum going to the United States.
Medical education suffers from the same lack of funds. Hospitals are inadequate in size and facilities; patients wait on cots in hallways and one may spend hours in waiting rooms. Family physicians are booked solid, and take few new patients, although the population is growing since the economy is booming. Specialist attention requires weeks, if not months, on a wait list. The oil millions-er billions- are not spent to allieviate the problem. Health care wages are low, much of the staff is immigrant, people with their first jobs in their new homeland.

Medicine is too expensive a career choice, and it requires long hours if one is compassionate; much better to go into engineering, geology, management, etc.