Working with a SIN number and a SSN number (Canada and the US)

I posted this on another forum.

Hello again,

Let me preface this by stating that, my wife has been approved as a sponsor! The documents are being forwarded to Buffalo! Hopefully it won't be long until I get my permanent residency. Anyway, now for another question.

I currently work in Canada on a work visa but there is a possibility to work for a U.S. company doing work online. So I won't be physically working in the States but they will need my social security number. My question is: will I encounter any problems while I am on a work visa in Canada with my temporary sin number and then working for a US company with my US Social Security number?

Would this affect my permanent residency application? I hope I have been clear. If I get my permanent residency and thus my permanent sin number could I work for a US company as well? The work is only part-time.

Thank you very much. This forum has been very helpful to me.