As you probably know, every state is represented by a number of members in the house of representatives and two senators. If you go to
www.house.gov
you can look up the congressman/woman in whoose district you live. At
www.senate.gov
you can look up who your senator is.
Most congressmen and senators have a local office doing 'case work'. They are helping constituents who have problem with federal authorities. Now, as you can't vote, you are technically not interesting for them. Most however try to be nice folks and have their casework staff help people who are dealing with CIS or DOS.
Once you know who your congressman is, look on his/her website under 'issues' and 'press releases' and 'sponsored bills'. You want to be sure that your representative is not a cosponsor of the 'kick all immigrants into the sea act of 2005' or the 'Do away with the H1b and L1 visa act of 2004.
Somewhere on their website it tells you how to contact their casework office. Usually you will have to send them a signed declaration that they are authorized to ask questions on your behalf.
Any federal office receiving money appropriated by congress HAS to answer to inquiries by members of congress. Usually their answers are meaningless. Something like: The service has replied that they will get around to your case eventually and that if you haven't heard from them after 60-999 days you should initiate another inquiry.
Now, as to the success of congressmans or senators intervention, opinions are split. Some people swear that the congressmans call managed to dislodge a case that has been stuck. Others are of the opinion that the congressional intervention has the opposite effect.