Stalling on Accepting Position...

I got a job offer this morning and should be THRILLED but I am too worried about quitting my full-time/GREAT insurance benefit position for a part-time every other weekend position that offers no benefits...I guess in my head I was thinking that I could do both but of course I can't because of orientation. In addition, I have an interview scheduled for tomorrow morning: a part-time position that does offer medical benefits. I told the HR mgr that I am very interested in their facility and that I would provide an answer "first thing tomorrow" which was DUMB because my other interview is at 10:45 a.m. and now I'm not sure how to stall a bit longer?! I don't know if it's acceptable to go ahead and accept this position, give my employer two weeks notice and then see how this other interview goes (and then if I'm offered that position and am more interested in it go ahead and accept and then regretfully "go back" on my initial acceptance?!). I know that it's too late to fix this (next time I'll just wait to call the prospecitve employer back I guess) but can anyone tell me if this is acceptable? Or is there another alternative that I'm not thinking about? I guess because I blurted out that I would let him know first thing tomorrow I don't want to be wishy-washy and call back and change it to Monday--but obviously I'm feeling VERY wishy-washy right now. Thanks to anyone who can offer me some advice!!