So it seems that the Courier gave Ulysses a package/letter before Ulysses allowed him to get shot, this information coming from one of his audio logs with Christine in OWB. I find it a bit curious that at Wolfhorn Ranch (Ulysses' Camp in translations) that there is a grave with flowers over it, and a radio next to it behind the home; anyhow Ulysses also said something along the lines of "He knows the way there" when refering to the Divide, so is it possible that The Courier at one point traveled through the Divide to the Mojave (or the reverse) to deliever something to Ulysses?
What do you think the package/message that impacted Ulysses life; could it have been information of a loved ones death (The grave behind the Ranch) that they were murdered or passed on?
Another thing to add onto that is that some people speculate that he is a Legion Frumentarii (Legion Spies), but in one of the Audio Logs he states blatantly that "There is no hope in the Bear, or the Bull." which obviously refers to the NCR and Legion, yet again comes another Flag Reference by Christine who says in both Dead Money and Old World Blues that he had the Flag of the Old World on his back...
In Honest Hearts however, Joshua Graham says he was expecting a different Courier (a Legion Frumentarii, one who poses as a Courier from time to time) to arrive in Zion (possibly to assassinate him [Joshua Graham]) rather then The Courier (The Player) so it may be possible that if Ulysses was beyond the Divide and a loved one died, he was gone because he was serving the Legion at the time.
Buuut IF Ulysses was indeed part of the Legion, something must have happened for him to shift his point of view from the Legion to the Old World; it may be possible that the Legion had his family/friend/relative killed to reinforce his duty and/or allegiance to the Legion being he would have nothing more to live for, but instead it backfired.
Ulysses said in one of his Audio Logs that "People are like Couriers, never knowing the message they bring", which could have come from experience with Courier Six (The Player) going to him with a message that had more impact then he knew.
Another thing, Ulysses supposedly came to the Big Empty seeking answers and History of America/The Old World and went directly to The Think Tank for them... yet he also went to an area containing a map finder/viewer and had sights on a location that some believe to be the Divide, in which Ulysses has said 'The Old World sleeps there' after Christine said "There's nothing there.", but yet like the Big Empty and the Sierra Madre, there are things that still lurk and lie waiting.
Now then, the Old World sleeping brings several ideas to mind in the form of people surviving; namely the 'Vault' project, or (I know alot of people hate the idea of it and despise it entirely) the Enclave... Now if the Vault Project was what he refered to, it may be a Vault filled with all the important people of America (Like Vault 0, which I believe was in Cheyenne mountain) or it may be a reserve of the Enclave who had civilians stockpile in one location as a secluded city inside a massive Bunker/Vault as safe stock or a pool to get soldiers/workers from.
The final thing I noticed and speculated on was the fact that Ulysses mentioned trying to bait the Courier into the Divide (albiet indirectly referenced), which points to the Courier facing off either Ulysses, or the Old World itself.
If there has already been confirmed facts and a background that is well known, my bad, if not then you should know again that this is speculation, so tell me what you think of my possibly terrible or maybe not so terrible speculation; also if some things arn't clear or understandable please ask what I meant and i'll answer it.