About zero. Americans are free to visit Canada for a maximum of six months at the sole discretion of Canadian Border Services Agency. Visitors may not attend school, work, or look for work while in Canada.
This includes living in Canada while working for a foreign company. Visitors may also not obtain social insurance numbers, driver's licenses, apply for health insurance, open a bank account, etc. Long stays or repeated border crossings will immediately trigger concerns by Canadian Border Services Agency. CBSA will typically ask for details about your 'visit' to Canada, why you are visiting so often, proof you are maintaining a residency outside Canada, proof you are employed (outside Canada), why you are able to take so much time off work, etc. Living with your girl friend is not a legitimate tourist activity.
They can deny you entry until they are satisfied you are a legitimate visitor, issue a visitor record (limiting how long you can stay in Canada), ban you from entering Canada for a year, and/or revoke your visa exemption status. If your girl friend could face up to ten years in prison is she knowingly aids you in staying in Canada while working -- or CIC would just cancel her permanent residency status. There are no 'live with girl friend' or fiancé visas for Canada.
If you wish to live in Canada, you would need to get married and have her sponsor you for permanent residency. Depending upon her status, she may not be able to sponsor you for two years after she obtained her PR. She must also sign an agreement assuming all your debts and must have a solid job history, minimum income, residency, and sufficient savings (starting at $13,000).
The process takes nearly a year.
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