I guess I shoudl have figured this out before I made the deal, but now I have to figure it out for sure..

I just traded for an arbitration eligible player. Our arbitration period is scheduled for tomorrow. If the trade doesnt go through before arbitration how does it end up working? Do I need to ask the other team to make an offer to him, or will I have a chance?

I've done that. If I want a lower amount--in other words if I want you give him less than what the player is asking for--I drop a TC to my trade partner and ask him as a courtesy if he would mind submitting (Specific amount here) on the player's arb. 99 times out of 100 your trading partner will be glad to help out. If you aren't fighting his arb figure, just let it go through.

I thought if he was arb'd it would void the deal since his salary changed? I've got the room to cover him regardless.

No the trade would only be voided if he went to arb and his salary put you over budget. Typically I decide whether I want to go to arb or sign the player to a long term deal and then ask the person he is currently with to sign him to a deal or submit an arb figure for me. I've never had anyone refuse and I of course offer to do the same in return when necessary.