Lateral Recruiting - Reneging Consequences

Hey guys, 

I'm an analyst 2 who recently received an offer for a lateral analyst position at a MM bank and the offer has an expiration of early next week. The issue is that I also have other interviews in the pipeline at significantly better banks (BBs) and they aren't really able to accelerate the process. Obviously, I would significantly prefer the BB offers if I am able to get those over the MM offer. 

What are the potential consequences if I renege on the MM bank offer after accepting it as a lateral analyst? Would the MM bank try to get revenge and notify my current firm about the fact that I have been interviewing / recruiting around?

Thanks.