If you really do not want to go to the border, you can apply outside Canada. You can not apply inside if you are a visitor, see http://www.cic.gc.ca/english/work/apply-who-eligible.asp
For the US, you can apply in any one of these visa offices: http://www.cic.gc.ca/english/information/offices/apply-where.asp#u
For example in Detroit, see http://www.cic.gc.ca/english/information/offices/missions/detroit.asp
According to http://www.cic.gc.ca/english/information/times/temp/workers.asp#west it would then take a month to get the work permit.
If you do it at the border, you would get it instantly but it is up to you.