Aside from the fact that this isn't really true seeing as the game plays fast and loose with the dimensions of the galaxy and those nebula are just pretty backdrops.... a nebula isn't indicative of travel over true interstellar distances.
The horsehead nebula is 13 light years across. The galaxy is 100,000 light years + across. Say it takes 5 days, optimistically, to cross the nebula - that would mean it would take 100 years minimum to cross the galxy - assuming you could get your hands on enough eezo for the trip. Which you couldn't, because it's too rare, and would be in even higher demand now.
And as has been said, the codex of the story itself implies the situation is much worse than that. Interstellar travel would be generational, largely impractical. If you can't get eezo you're restricted to sub-light speeds because the mass effect is needed to achieve FTL. For those in the Sol system with only military resources, and in systems now dependent on interstellar trade, it is a death sentence.
The codex listed speed for standard, non-Relay FTL is "a dozen light years per day." Given the size of the milky way, that means a ship could travel from one edge to the opposite side in roughly 30 years. There are 22 stars within a day's travel of Earth at that speed. There are over 50 stars within a day and a half of Earth. It shouldn't be terribly difficult to leapfrog from system to system through the Local Cluster.
Also, from what I've heard around these boards, Eezo is not spent as fuel, they only need a certain fixed amount of it to engage FTL, which they already have, and what is actually "burnt", requiring refueling, is just standard combustibles like Tritium, which is a fairly common element in the universe that they could find easily enough along the way. They can probably colect quite a bit of it from Jupiter alone.