Since you haven't actually committed to these people you may still negotiate, yes. However, be ready to potentially have this offer withdrawn. If you're ready to potentially give up benefits, paid vacation time, and a short commute, then here's what you should do:
Go back to your recruiter and tell him very politely that you have another offer on the table, and that you feel that a slight bump up in pay would make you far more likely to accept their offer over the other one:
Hi, insert name here. I'm very excited to have gotten your offer! Thank you for your trust and consideration. However, I've also received another offer for, I'll be honest, significantly better pay. I have to admit, I would much prefer to work for you guys, however I'd love it if you guys could bump up the offered amount a little bit. I apologize for throwing you a curve ball, but please let me know if that would be at all possible within the next 24 hours or so. Thank you very much!
On one hand, they already have their hearts set on you, so you have a pretty decent chance of simply getting the extra 10K. On the other hand, some people may think that you're being disingenuous by changing the terms this late in the process, and either reply with a "take it or leave it", or simply retract the offer altogether.
At the end of the day, it's one big gamble, but you're in a pretty good position for it.