My current employer requires 30 days' notice when resigning. I recently interviewed with a new potential employer and during our first interview, I mentioned this to him and he stated that it was "extreme." He told me it could probably be stretched to 3 weeks by handing in my resignation when I receive the offer, PRIOR to my background and drug test being done (I'm not worried about the results of either in the slightest bit), but it seems like a risk in the sense that I could essentially be resigning from my current job without yet having an iron-clad offer in writing with a new employer? Is there any way they could back out of the agreement even when my background/drug tests come back clear?
I don't want to leave my current employer hanging, either. They are a small company and will surely feel the hit if I leave and would even have a hard time transitioning my work to someone else in a month. I'm not angry with my current employer - I'm just looking to advance my career and proceed on the right path. What is the best way to proceed in this situation?