A foreign national can be sponsored by a Canadian to come to Canada to live, but it is very expensive and time consuming. The marriage can take place and then the Canadian can sponsor her/his spouse, but again, it is quite involved as Canada only accepts spouses on a 'point system'.
A person living in the US under TPS has only 6-18 months of temporary status and the status is NEVER extended and it never leads to permanent status, (ever). It is only issued in the case of extreme emergencies (such as Haiti's earthquake) and therefore, one should not assume that because they are living in the USA that it will be anything other than temporary.
If the TPS marries a Canadian, they cannot enter the US because the TPS has no citizenship nor rights under the TPS to sponsor anyone.
If I understand you correctly, you are hoping to enter Canada as the married spouse of a Canadian, which is permissible, but you can only apply for citizenship from outside the country, regardless of the fact that you are married to a Canadian. And while awaiting approval, you must stay outside the country of Canada. (sometimes many years.)
The best would be: check out what exactly is required in the points that you may have, and see if you will qualify. Then, decide if you really want to live apart while married for so many years. As the TPS is only temporary, your TPS status will probably run out long before you will be allowed into Canada, so it seems unlikely that even marriage can help you, unless you are prepared to live far apart. Illegals in either country is dangerous and may mean jail time so it is not a good thing to risk although many do it.