Form 2555 is only used by non-resident US citizens or LPRs, which you aren't. You would use Form 1116 to claim a foreign tax credit for Canadian
taxes if you are a US resident taxpayer, however the tax credit most likely wouldn't cover the full amount as Canadian tax rates are higher, so you would still end up paying the total of the Canadian rate on Canadian-source income.
If you have Canadian-source income you still have to pay Canadian income tax on it and also CPP/EI withholding if it's employment income, the only difference is that you use the non-resident T1 instead of the resident one. Also your payroll claim code is 0 instead of 1, you have to submit a new TD-1 to your employer, I'm not quite sure how that affects your taxes though, there is a change but I can't remember what exactly. (This assumes the work is done in Canada, otherwise you would have to be on a US payroll).
You don't save any money by moving your tax home to the US though if your income is largely Canadian-source.
My personal view is that's not a good idea to move your tax home to the US if you're in TN-1 status for a number of reasons. The first is that TN-1 requires your stay to be temporary, which implies residence abroad. If you're filing as a resident in the US that plays against that and it could cause you problems.
The second problem is that if you are ever denied entry, you automatically revert to being a resident of Canada which means you have a sizable chunk of paperwork to do.
The third problem is that the amount of paperwork involved in moving your tax home to the US and then moving it out again is substantial, several times on here I've tried to cover all the forms you need and I'm still not sure I've got them all, but it's a lot. Just no point doing it for a stay that doesn't involve at least one full calendar year. There are also a lot of non-tax forms you may end up having to file like the FinCEN FBAR form to declare your foreign assets.
In your situation you've got another problem, because if you're a student (J-1) you usually receive money from abroad. If you're filing as a resident and someone sends you money from abroad (e.g. your parents) you have to pay US income tax on it. If you file as a non-resident using 1040NR and 8843 you're basically exempt from US income tax, except on US-source income, and even then, as a student you are exempt from social security and medicare withholding as well.
As a student you are definitely better off filing as a non-resident.
The only real advantage to filing as a resident is if your income is mainly US-source income, because US income tax rates are usually lower (but not always, if you're from BC and you live in MA or CA you may find the BC rate is actually lower depending on which bracket you're in). So you don't end up paying Canadian income taxes on top of what you've paid in the US (minus the foreign tax credit).
Whether that is a major advantage or not depends on your income. If you save huge amounts doing it that way then it's worth the hassle of all the paperwork and so on. If you're saving small amounts (or even losing money) then obviously it's not.
Other problems you might have moving your tax home to the US is that you can't contribute to your RRSPs and things like that anymore (not easily anyway, there might be a way of doing it) and TFSAs would become subject to Canadian income tax again as Canadian-source income as the tax exemption only applies to resident taxpayers.
Steve.