To echo some previous comments, having a publication is great. But, more important is whether or not you can articulate your project(s) and your role in it, how the work you did fits into the greater picture, and the content and quality of the letter you get from your research mentor (or mentors, depending). Admission committees will know that much of what determines if you end up getting published is luck--at all levels of research but certainly at the level of an undergraduate student. Although some time has passed since I applied to MSTPs, I didn't have anything published when applying and that was never a problem.
In fact, now that I think about it, the more complete your autonomy on your project, I would guess the LESS likely you are to actually have it published by the time you apply. A more likely publication would come out of work one might have done just by helping an established graduate student or postdoc finish up something that was nearly complete anyway. Just a thought.
