Honestly, I never believed that Senator's office could help. All they can do is an inquiry for you. There's only few things that can hold up your case. Most common is the FBI Name Check, where nothing can be done, or at least I haven't seen anything here. Then I believe is the FP, usually expired FP1 which holds up the case until FP2 is completed - the Senator's office can tell you when to expect the FP notice.
Again, from what I've seen here, and experienced myself, they can't expedite the case just for no reason, especially when it's current. If your case is cleared all security checks and FPs but it got put in a pile waiting for it's turn, here Senator office can kind of remind them that your case has a RD of earlier than the current processing dates. Then the standard reply is, "your case will be assigned to an immigration officer within 60 days, but this doesn't guarantee an approval".
That's about it.
My case is way behind, and they still can't do anything about. I've talked to Senator/Congressman over 15 times all together, and unfortunately they just have no power to do anything, but provide you with some information on the status. I don't know if I needed all the details, especially if I can't do anything.
From what I've seen/learned here, the Senator's office works with a CIS staff designated to provide info to gov. entities. This staff, doesn't deal with adjudication of cases, but only provides status. I'm not sure if this staff actually deals with IOs, I think they maybe only have access to the internal file so they can observe the progress. I believe the LUD doesn't change when this staff looks at your file, or at least I haven't heard/read of any instances. This to me is a proof that they can't really do anything about your case, whether the Senator's office insist or not. At the end, the Senator's office will not jeopardize their relationship just because of your case. Once approved, you will disappear, maybe even forget to say thank you to them, so why bother.