From a tax standpoint they either have to have an EIN and do US withholding taxes, or else you have to register as self-employed or start an S-corporation. Which basically means you invoice them as an independent contractor and do all the withholding
taxes etc. yourself.
If you're self-employed then you have to get a self-employed healthcare plan.
Essentially if you move to the US, you are a US employee, so they have to act as a US employer and comply with US tax laws or you have to set up your own company or be self-employed.
I think if you go the self-employed route you have to file a non-resident T1 return to report Canadian-source income, and if you set up an S-corporation it may have to file a T2 return as a non-resident corporation. However these are merely informational returns, provided all the work is done in the US you do not have to pay any Canadian income taxes.
This all sounds complicated but believe me it's trivial compared to the complexity of doing some of the work in one country and some work in the other, because then you have to proportionally pay tax in each country. The only exception is if you are directly employed and stay for 90 days or less and earn $10,000 or less. E.g. you set up a US corporation, it directly employs you, and you have to work in Canada for a short period. Provided you're in Canada for less than 90 days and you earn less than $10,000 while in Canada, you do not have to comply with Canadian withholding laws.
Steve.