This is what I am thinking was going through their heads:
President-"Men, nuclear war is undeniable. It will happen, and it will happen soon. So I've made a contract with a company, a company called Tec. Vault-Tec. They will build sprawling underground bomb shelters, called vaults. And they will preserve America's great citizens, and each Vault will have a unique purpose, a test, to see how humans react under certain conditions. Afterwards, we will collect this data and observe them."
Workers-"That's a great idea! Amazing! No faults at all!"

Now here's the rational response:
"WHAT THE [censored] ARE YOU THINKING? You want to TEST humanity in insanely...inhumane ways so we can collect the data WHEN WE'RE ALL DEAD? Are...are you smoking something? Is Vault-Tec real? You have got to be kitten kidding me! YOU ARE [censored] INSANE, MR. PRESIDENT. [censored], INSANE."

Seriously, what is the point of the Vaults? Why are they there? To test humans under stressful/relaxing circumstances? But why? The employees are likely dead! How would they collect the data, and if they weren't dead, WHY?

Blame the enclave...

It was done because they could. The Enclave wanted to use the vaults to test things such as less food could be produced, dimmer lights and ethnic diversity. Then fallout 3 and new Vegas came along and the US Army seemingly used a Vaults 87 and 92 to make super soldiers and the Enclave are apparently just sadists :shrug:. Whole thing was rotten from the start.

Being cut content and all, but in Fallout 2 it is stated that the Enclave's original plan with the vaults was to test the subjects in insane conditions as the Enclave intended to leave Earth for some other planet in case Earth was rendered uninhabitable. It wasn't, and so Enclave stayed and it looks like they never utilized the vaults' results: Only Vault 13 appears to have been contacted with (and attempted with Vault 101)

America probably thought that there was absolutely no hope for humanity, so decided to have some fun with them in Vaults while they still could.

If anything, the contracts that people probably signed to enter the Vaults could have even described in fine print the true purpose and the risks of them entering. People may have been too obsessed with their safety to actually read it. The same way most people on the internet don't read the Terms & Conditions.

Some may have been invited to Vaults, like 21 and 92. Who would turn down that invitation? Again, people are too obsessed with their safety to think of anything but. Remember, America was classed as paranoid, it's only natural that it's people probably were paranoid too.