You need to go to a consulate only if you need a new visa. If you already have a valid work visa on your passport and you have a visa to enter the United States, you may simply enter USA, make a u turn and return to canada. At the border present your new LMO and offer letter and they will provide you with a new work visa right away.
I am told by my lawyer that this is possible however i have not experienced it. I have also not come across any forum members who have done it.
Alternatively, you may send you docs to Alberta to get a new work permit.
Hope this helps.