muhiretomas

Well, I can report that it appears a Senator's inquiry can change the whole course of a case in certain circumstances. Let me explain:
After the Senator's office sent their inquiry to the NVC, they received a reply saying that the NVC had completed our case and was only waiting on an interview appointment to become available at the embassy. My guess is that the NVC "completed" the case AFTER they received the inquiry from the Senator and covered themselves by saying that it was the embassy's wait times that was delaying the case from moving forward. The NVC had never indicated to us that our case was complete, and in fact ceac still shows an incomplete case. To me that seems to suggest that the Senator brought the case to the right person's attention, at which point they quickly completed the case and put it in line for an interview appointment.
I anticipate an interview appointment soon and will keep all posted as to further progress.
All in all, I would recommend contacting a your senator or representative as soon as there is an unreasonable delay or problem. It is in these moments that they can bring your case to more immediate attention of the people reviewing cases.
Best of luck!

You can contact either US Senator for Illinois by going to their respective websites and filling out an inquiry form explaining your issue.
For Mark Kirk, go to http://www.kirk.senate.gov/?p=federal_agency_help. Fill out the form and his immigration liaison, Elisabeth Conklin, will contact you, asking you to fill out a privacy release form that allows her to ask about your case.
For ####### Durbin, go to http://www.durbin.senate.gov/help/services/immigration. His site has a specific form for immigration issues and you will be able to fill out and send the privacy release form by fax or mail. After his office receives your inquiry and your privacy release form, his liaison Tran Nguyen will contact the immigration office on your behalf.
I contacted both Senators at the same time, and each was able to get me an answer from the NVC in about two weeks from when I contacted their offices. It seems that the inquiry from a Senator brought the necessary attention to my case which should have been completed a month ago.
Now just waiting on the interview appointment.....
I hope that you find the same success with your case. Let me know if you have any other questions.

Thanks for the reply. I assumed that they may not have too much power in a case, but making prompt contact is exactly what I am looking for.
Calling the NVC results in one of two responses: continue waiting or submit the case for supervisory review (which is a "reassuring" way of saying "continue waiting"). Given that my case is near complete, in that all documents are submitted, fees paid, and application submitted, I feel it is only a matter of the case being brought to the attention of the right person for a quick review. If a Senator at least has the ability to bring the case to more immediate attention (not the 42 days required for Supervisory Review), that is all I would ask for.
I will let you know how it goes.

Well, I can report that it appears a Senator's inquiry can change the whole course of a case in certain circumstances. Let me explain:
After the Senator's office sent their inquiry to the NVC, they received a reply saying that the NVC had completed our case and was only waiting on an interview appointment to become available at the embassy. My guess is that the NVC "completed" the case AFTER they received the inquiry from the Senator and covered themselves by saying that it was the embassy's wait times that was delaying the case from moving forward. The NVC had never indicated to us that our case was complete, and in fact ceac still shows an incomplete case. To me that seems to suggest that the Senator brought the case to the right person's attention, at which point they quickly completed the case and put it in line for an interview appointment.
I anticipate an interview appointment soon and will keep all posted as to further progress.
All in all, I would recommend contacting a your senator or representative as soon as there is an unreasonable delay or problem. It is in these moments that they can bring your case to more immediate attention of the people reviewing cases.
Best of luck!