My new employer hasn't been able to get a previous employer to confirm I worked there. How likely is it that I'll get let go?

On my resume I put my last 5 years worth of jobs on it. I'm 25 so haven't had many jobs. The company I'm employed with right now, my first day was August 1st. I had gotten an email mid July asking for # for the employer in question. Gave it to them, weeks later they asked for it again, I gave it to them again. Started work like normal, then the lady handling backgrounds said some of us didn't finish them and to go with her to do so now. She didn't call me so I figured I was safe. Now it's back to if I don't get w2s from them I risk being termed. That job was my 2nd job. I had quit school, right away got a job, quit the job to go back to school, found I needed a job lol and worked at the job in question for a few months. It was a fast food place, in no way is my current job anything like a fast food place so I don't see why they'd care so much about it. Problem with getting the w2s, I don't have a car I take the bus to work, I could try to go before work but that'd be cutting it close. After work is when they're busy. Went tonight was told to.go back later. So, I'm stuck