Joker 2
The implication I've been getting is that Ulysses is an Enclave Remnant. So I'm starting to think that I, or rather The Courier, also used to be an agent of the same, rather inauspicious, organization.

Based on the information given out during New Vegas, the add-ons we've had so far and some press for Lonesome Road, Ulysses has been going around to various organizations to try and figure out which one he should back as the best hope for the future of humanity. It seems he isn't entirely down with any of the options currently available. (The New California Republic and Caesar's Legion, as well as the Brotherhood of Steel have been mentioned specifically as contenders. No mention of The Followers of the Apocalypse has been made. Though that's not surprising as it seems they're not interested in building societies, but only working within them.)

3 of Clubs

In Honest Hearts, Joshua Graham suggests that he expects Ulysses to come looking for him. The impression I got is that Joshua thinks it would be in an attempt to kill him. So why would that be? Is it because of a connection between the two of them during a time when they were both part of the Legion? Or did Ulysses also consider joining up with the New Canaanites at some point?

Meh. Who knows.

I was thinking possibly that, unable to find a society he actually agrees with, Ulysses is looking to start his own. Possibly using The Divide as its starting point. Great way to build power without being bothered, finding a place people think is uninhabitable and making it habitable without telling a whole lot of people. He clearly wants to show the Courier something, possibly have some kind of influence on who I/he/she supports in the final conflict of the game? Narration from the end of Dead Money indicates some kind of battle between the two, but he just doesn't sound like an angry dude.