uptik is totally right about it. at work, my manager care jack shit about anything, as long as she is getting pay (for not doing a damn thing, she doesn't know how anyway) and have a scapegoat to cover her ass. Guess what, she fock up the account, and the company gave her a promotion. I have no faith in this company anymore.
I'll also give you a bit of advice for when you start your career. If, when you first start, you are approached by someone in your company who says that they wish to help you, and that their ''door is always open to help a new guy", politely thank him/her and stay far away for the remainder of your tenor. These people only wish to exploit you. They are easily identifiable. Often with a self-perception of being the "most experienced". They will shower you with advice and compliments. However, they are nothing but venus fly traps looking for their next meal. Good luck.
If this is a real job, ie not a prop trading slot, I have to agree with the above advice. I'm more cynical than most and have the scars to justify it, but doing the right thing is never wrong. In addition to asking the first firm for more time, you might ask the second if they could move up the interview date because you are getting pressed to accept an offer. Knowing that someone else wants to hire you can only make you look better to them.