If your spouse is a temp worker, you both have the same status in Canada - i.e. temp residents allowed to work. You certainly can apply for any PR program but that comes with its own requirements and processing times e.g. CEC is a faster program used by many who have already worked in Canada in a skilled job, but that requires one year of full time experience completed to apply.
Your SOWP will be of the same length as that of your partner. A temp worker is eligible for some of the necessary things, but not others.
E.g. the Canadian ID number that you mentioned is called SIN (social insurance number). You can get that a day after landing. But you will be issued a number that starts with 9. This is an indication that you are not a PR and a temp resident instead. You can open a bank account using this (or even without this by just showing your passport, work permit and job etc.).
But you would have a really hard time getting any credit item such as a credit card or a car lease. For credit card, banks would ask for secured credit card (i.e. deposit the full balance of your limit as security) and no car lease would be issued beyond the expiry of your work permit. Since car leases are usually longer than two years, you would face a much higher monthly payment and interest rate. However, you can still get health card (valid only for your wp period) as well as driving license.
To cut it short, you can maintain a life but don't expect to receive much credit unless either you become a PR, or you have lived and made a good credit history for at least two years (on a secured credit card). The only way to get around this for e.g. for car lease is to find a co signer, some one who is a PR with good history and vouches for you i.e. if you default or leave the country, that person would have to fulfill your obligations instead.
Hope that helps.