From what I have researched on the CIC and read on this forum, you cannot obtain a visitor visa for Canada unless you are planning on leaving Canada eventually. Plus if you are an American citizen you do not require a visa to be in Canada. If you plan on being there permanently, you need to find some other option.
I am in a similar situation...My Canadian husband and I got married and are living here in the U.S. together and hope to move to Calgary within the next few months. I am trying to figure out a way that I can move up there with him and still be "legal." We are planning on starting the application process outside of Canada, which is a faster option. But eventually I would like to move there to be with him, but we don't know how long the application will take, so I am trying to find a way to be up there while the application is still in process...
If you are in Canada, you may call the CIC Call Centre for some advice on your situation. The phone number is 1 888 242‑2100 and below is the link to more info:
http://www.cic.gc.ca/english/contacts/call.asp