What kind of financial liability and responsibility will I be exposing myself to if I accept a treasurer position?
We cannot give legal advice. The following is not a substitute for the advice of a local attorney. But we hope the information will be useful.
The first rule of corporations (assuming the company you work for is indeed a corporation as you imply, rather than a sole proprietorship) is that owners are not liable for the debts of the corporation. You are not even an owner, but an employee - which makes you even less liable than an owner (and owners won't be liable if everything is above board). As long as you don't personally guarantee any debts (meaning to promise to personally pay the debt if the company cannot pay it), then you should be shielded from any financial liability - provided you have no knowledge of a failure to maintain minimal corporate records and no knowledge of any intentional wrongdoing on behalf of the owner or anyone else.