Please let me know if you spot a mistake in the caluclations, or know of a better canon figure to use.
There are 122 vaults, with an "normal" designed capactiy of 1000 inhabitants. Thats 122,000 people saved at maximum capacity.
Wikipedia gives 308 Million people living in the USA today. Lets be ultra-conservative and assume that the US population at the great war is the same as it is in the real world today (that for some reason or another the US's population in Fallout's world before the bomb grew a lot slower than in the real world). On that figure, 0.03% of the population can fit in them ( *Much* Better chances getting a spot in a lifeboat on the Titanic).
Vault 13 we know how much cost to build: $645,000,000,000 (645 Thousand Million, or 645 Short (American) Billion). Assuming that this figure is similar across all vaults, thats $78,690,000,000,000 total cost of building the vaults. The total costs is almost Seventy Nine Thousand Billion Dollars. Each Inhabitant's survival costs 645 Million Dollars!
Fair enough, these figures do not include inflation. There is only one thing I can think of that has a Pre-war price established in canon, that has a comparable product available today - The Family Car. We know a Chryslus Corvega had a list price of $199,999.
Granted, this comparison isn't ideal - In a war economy, the materials to build the car are likely to be more expensive and scarce as more and more resources are pushed into building the tools of war. Add to this many Chryslus plants being drafted in to make military vehicles and other equipment means that stocks are going to be scarce, pushing up the price of the car even more in respomse to demand - given that the average family's gasoline car is at that point useless except as scrap, I can see an Nuclear car being particularly desirable! However, on the side that maybe this is a reasonable figure, the stuff that goes into making a vault, the electronics, metals, etc, are probably also in demand by the military, as are the factories that make those things.
In any case, its the only number I can think of that we can compare, and gives us a conservatively high inflation rate.
I've just had a quick look online, and a ford dealer in Manhattan puts the list price of a Ford Taurus at about $37,170 (I'm happy to consider other figures if folks think they're fairer). That puts an inflation rate between our world and Fallout's at the time the bombs dropped at about a factor of 5 (a shy over 538% to be exact).
Based on this number, each vault costs about $120 Billion in todays money. Fourteen thousand six hundred and forty billion US Dollars for the whole project. The US Department of Defense's annual budget in 2009 is $651 Billion. These figures at face value say the US Department of Defence today could fund about 5 vaults a year if it spent nothing on anything else, no troops, no civil servants, no ships, no guns, ammo, etc... Project Safehouse from start to end has the same cost as defence budget over 24 years.
Is saving about 0.03% of the population worth that much money? Would a politician (President, Senator, etc) who is making a decision to save the american people going to think that the vault project is good value for money? At 1000 people per vault, 5 vaults per year, it would take 61,600 years to safely house the 308 million in vaults, if I've got my figures right.
Unless there's another reason to do it, The vaults as safe houses simply do not make sense.