My current employer is offering the option of working remotely with a corporate restructuring this summer. As someone that is starting to get pretty tired of Canada's cold winter, I was looking to take advantage of my employers remote offering and look to reside in the United States to avoid the cold weather. From my understanding, I wouldn't need a TN/H1B as I'd be working for a Canadian company, but I'm uncertain as to what I'd need, if anything to be allowed to reside there for long term. Could anyone shed some light on this for me?
Your understanding is incorrect. To legally work in the US you need a proper immigration status. If you don't have a US citizenship or permanent resident status (green card) - you need an immigration status that allows free employment.
Since you're working for a Canadian employer, located in Canada - you won't be able to get neither H1b nor TN. You'll need to have some other way to sponsor yourself into the US without being dependent on an employer yet with a job authorization. Options are marrying someone. Either a student, or someone on L1 visa, or a green card holder, or a US citizen. Or taking a full course of studies in a US university and then working for that Canadian employer as part of your OPT.
It's much easier to get B1 for telecommuters: http://www.immihelp.com/business-visa/permissible-prohibited-activities.html