employment at will when the employee quits

Most questions about at-will employment talk about firing people. My question is about quitting.

I just quit my job this morning. In the contract I signed last spring, it states that I have to give one month notice (language below). When I told my employer that I couldn't give a month because my new job started sooner, she threatened to sue me. From there the conversation got ugly, and I ended up quitting on the spot. My question is: does she have any legal basis for suing me? I work at a private, non-unionized, for profit firm in Vermont.

The contract states:
should an employee decide to terminate his/her employment with the company, written notice of intent to terminate will be given at least one month prior to the final departure date. During that time, the employee should be prepared to make arrangements to finish all tasks on hand and/or to provide a detailed record of tasks still outstanding/to be done. Further, the employee is expected to make arrangements to train his/her replacement, whenever it is mutually convenient for all concerned.