Lburg..as others noted, it depends. Most companies indemnify their engineers for errors and omissions; however, in many states, the engineer may have joint and several liability with the company, so yes, they can sue you and yes, you can be held liable.
Should you rush out and get E&O insurance on a personal basis? I would not. I have worked for large and medium sized engineering firms and have owned my own firms. With my own firms, I have (and have had) E&O insurance for the company that covered me. The same was true of the firms for which I worked, and I work in a state that allows the engineer to be sued separately for engineering acts.