The house only matters if you make a capital gain on the sale of it. Otherwise there is no tax.
You basically have two options if you are on TN-1, move your tax home to the US or keep it as Canada. My advice is always to leave it as Canada because the paperwork is much simpler, plus you must have "non-immigrant intent" as TN-1, plus you don't suddenly find yourself stuck in an awkward situation if you are ever denied entry.
However I have to say hardly anyone ever bothers to listen to me because you save a lot of money on
taxes if you move your tax home to the US because their rates are lower.
IRS publication 519 explains it all in detail, and this CRA document:
http://www.cra-arc.gc.ca/E/pub/tg/p151/README.html gives a basic overview of it.
If you file as a Canadian then the house is treated exactly the same as if you lived in Canada still, i.e. if it's your principal residence there is no tax, if it was a second home you pay Canadian capital gains tax on any gain.
If you file as a US resident tax payer then obviously it cannot be your principal residence so you pay Canadian CGT and tell the CRA you live in the US and you also pay US CGT and eventually you will get the Canadian bit back from the CRA.
Obviously if it's your principal residence and you've made a substantial gain on it, it's better to remain a Canadian resident tax payer until you've closed on it. You can file as dual-status, i.e. remain a Canadian tax payer until such and such a date then move your tax home to the US, but this does entail you filing at least three tax returns, i.e. a T1, a 1040NR for the portion of the year you were a Canadian tax payer and a 1040 for the portion of the year you were a US tax payer.
Publication 519 explains this at great length.
My advice though would be to remain a Canadian tax payer for 2009 given the US economy at the moment. If you get laid off all you have to do is file a 1040NR and an 8840 for the portion of the year you were in the US, that's it.
US employers sometimes don't like people filing as non-resident as they have to do withholding at a higher rate, but it's not terribly complex - read pages 22-26 of IRS publication 515.
Steve.