"Administrative processing" covers many things, from security checks to investigative functions. There is very little that can be done by you to move things. In these circumstances, it is unlikely that the Consulate will issue the H4 unless the H1B is withdrawn.
Since it is likely that your wife's prospective employer retained an experienced immigration attorney to assist in the H1B filing, the best person to ask these questions of would be that lawyer. Speak with him/her as soon as possible.
This answer is of a general nature and should not be relied upon as final, nor is it intended as legal advice. A consultation with an experienced attorney is always the best way to go.
I agree with my colleague. "Administrative Processing" is a general term covering many things from security checks to processing functions. Generally, there is not much one can due to move a file along at that point. In this situation the Consulate will not likely issue the H4 unless the H1B is withdrawn. Check with your companies immigration attorney, or your own, to determine how best to proceed. Good luck!
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She may apply for H-4 however if it is a related issue, the H-4 will not be approved.
This response is general in nature and cannot be construed as legal advice, given that not enough facts are known. Any comments offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship. If you would like additional information based on this response, please contact my office at 510 657 7665 or 415 902 0832 to schedule a consultation.