Yeah I know, that's his quote about him believing in pre-war America.
His quote from the card is, "The day I set my flag down it'll be over my body, or over a nation I believe in." The Old World America is that nation he believes in.
Here's my theory: Ulysses was originally a Legion Frumentarii disguised as an NCR soldier, until the company he was infiltrating reached a place known as the Divide and (I'll quote the wiki here)
Some terrible events happened there in the past, splitting the earth, destroying entire NCR companies and cutting off supply lines along California State Route 127, and State Route 88, which allowed Caesar's Legion more time to recover after their loss at the First Battle of Hoover Dam.
It was here that he found some memory of the Old World hidden in the ruins and storms of the supposedly empty Divide. It was believed that all the NCR soldiers died at the Divide and survivors were only a legend (just like the Sierra Madre and the Big Empty and the survival of Joshua Graham were legends). Now here's what I think, Ulysses somehow survived what happened at the Divide and he learned some secret about the Old World (He did say he wanted to "Show the Courier what had happened there") and began to see the flaws in the Legion and became loyal to the Old World after he found a possible way to restore it.
He went searching for answers about something at the Big Empty eventually in his new quest to(House's securitron army possibly?).
Ulysses being an ex-frumentarii would explain why Graham thought he would come to assassinate him (Graham had lost contact with the Legion after the first battle of Hoover Dam, the same time the NCR company Ulysses was infiltrating had gone missing, thus explaining why he didn't know of Ulysses' new loyalties). Somehow the Courier is going to play into this and apparently has delivered a message to Ulysses before, either directly or indirectly, and Ulysses wants to show the Courier the glory of the Old World and how it can be restored. The Platinum Chip will play into this somehow (maybe Ulysses *wanted* Benny to get his hands on it? Possibly he somehow knew the Courier would survive? Maybe *he* was the one who placed Victor there in the first place long before House came along somehow
knowing House would later use him to save your life?)
Edit: I'm going to re-post this all in my Lonesome road speculation thread.