It depends.
FOR EXAMPLE, in a hospital, an employer may have the right to ascertain whether or not its nurses will be going on strike due to staffing issues. However, they have to tell the nurse why they want this information, they have to make clear that the nurse need not answer, and that the nurse will not be retaliated against. The question must also ocurr free from employer hostility and must not be coercive. So long as this notice is given, the employer MAY be able to legally ask, at least in a hospital setting, whether an employee intends on participating in a strike.
However, if the employer is simply asking you about your intended union activities, then it could be a violation of Section 8 (a)(1) of the National Labor Relations Act. This section prohibits employers from interrogating employees about their union and/or protected concerted activities.
I would advise you to contact an Information Officer with the National Labor Relations Board asap and discuss your case in detail so that they can competently address your question. You have 6 months from the time that the incident occurs from which to file a charge (otherwise it will be barred by the statute of limitations).
The NLRB is the agency charged with investigating these types of issues. There is an office in every state. Go to www.nlrb.gov for the number to your local office. You can also go to that local office M-F from 8:30 to 5:00 and they will see you within minutes. They always have an Information Officer to attend the public.
Good Luck