You can apply at the border for a work permit. I spoke to a lawyer about this and he said it was very unlikely that someone would get rejected at the border. However, the above poster is wrong: you can apply inland to adjust your status, even if you are a visitor. From CIC's website(for some reason I'm not allowed to post links, sorry):
This application is for temporary residents who are already in Canada and wish to:
extend their stay;
change the conditions of their stay;
change their type of temporary status; or
correct problems with their status.
It is important to apply for the renewal before the expiry of your current status.
New: You now have two options available when submitting an application to change conditions or extend your stay in Canada as a worker:
Option 1
Submit your application electronically
or
Option 2
Download and read your instruction guide and your application forms
Complete, sign and date your application forms
Pay the fees
Mail your completed application to the Case Processing Centre in Vegreville, Alberta
Visitors are considered temporary residents.