It’s still an open question how much water there is on the moon. If there’s enough, you can certainly make rocket fuel on the moon.
However, one thing we do know about the moon is that there is a LOT of oxygen in the Lunar regolith. As much as 50% of the regolith is bound oxygen. So that gets you half your fuel right there. Now you just need something to burn. Hydrogen would be ideal, and if there’s water we can get plenty of that.
I can easily see an infrastructure like this: Mars spacecraft is launched from Earth in pieces to lunar orbit, where it is assembled. Lunar base creates rocket fuel, and sends it up from the moon’s surface to fuel the spacecraft in orbit. If we can’t find enough water, you should send the Mars craft up with pure hydrogen aboard, and then fill the oxidant up from oxygen processed out of the regolith.
Another big part of a martian spacecraft would be the shielding required for the crew. That’s heavy, and very expensive to launch from Earth. But you might be able to send up a double-walled spacecraft, and then fill the space between the walls with material mined from the moon.
Then of course there is food, which could be grown hydroponically on the moon.
So I think in theory it makes sense to provision and launch a ship from the moon’s orbit. In practice, however, this all sounds hideously complex, and I don’t think this kind of large-scale manufacturing is going to be done on the moon any time soon.
Anyway, it’s kind of a mistake to consider this whole program as only “Building a moonbase, then a Mars ship”. That’s the ‘hook’ Bush put on it, but it’s really about a lot more than that. It’s about redirecting the majority of NASA’s effort to the exploration of space instead of commercial space launches and ISS maintenance. The new ‘vision’ also involves robotic exploration, space telescopes, etc. Basically, the exploration budget goes from a small fraction of NASA’s budget today to being about 80-90% of the budget in the future. The Crew Exploration Vehicle is only about 20-30% of that budget.