OPT extension requires e-verify number of your employer. My spouse also got RFE during extension because the e-verify number he provided wasn't correct (his employer didn't know which number it was, so gave the wrong number). But, once he provided the correct number, his extension was approved within a week they received it. He received RFE by mail within a couple days of it appearing in the USCIS website, sent new info the next day it was received.
I have also heard of other people receiving RFE for fingerprint if you submitted the application online, and even in their cases, extension was approved about a week after responding. 

Since you don't know what the RFE is for, I think the best thing for you to do is to wait for it. Explain the situation to your (potentially) new employer and buy some time if possible. And then take steps depending on what the RFE is for. If it is something minor, it should be cleared pretty easily. But, since the extension is based on your current employer's e-verify status, I think it is best if you change job once you get the extension.