It has been awhile since i have been that low but expand slowly ... you didn't say which resource you are running out of that is causing your vault to fail. I published some hints in other threads on Deathclaws but here are a few more targeted at the low end player:
- build at least one of each room as soon as you are able (keep them at level 1 for awhile as a level 1 room results in less powerful fires, radroaches, and molerats ... a single room is better than no room ... go double when you can ... triple when your money permits ... don't upgrade any rooms except key ones until mid game
- make your pregnant dwellers work (they don't need to stay in the living quarters while they wait to deliver the bun in their oven) ... don't put all pregnant women in the same room as they will run if anything happens (spread them out in all the rooms)
- rush rooms a lot at the start (especially if you have level 1 rooms so the impact of failure is lower) ... rushing give you free experience and caps plus the extra resources
- be careful where you put living quarters as they are more difficult to move around, but build whatever rooms you need ... if you need extra water build an extra room (you can always demolish it later)
- keep at least one dweller exploring wasteland as much as possible (it is the best way to get free caps, free weapons, and free outfits) ... work your way up to keeping a dweller out for extended runs once you get sufficient weapons and outfits for all dwellers ... key timed events occur at 20, 30, and 60 hours ... the benefit of staying out past 60 is minimal until the end game
- complete reasonable objectives to get caps and lunchboxes ... kill unreasonable objectives using the daily skip one objective
Hope those are helpful. If you have more specific issues I could respond more specifically