I would not rule out the chance to preserve a nucleus of human specimens. It would be quite easy... at the bottom of ah...some of our deeper mineshafts. Radioactivity would never penetrate a mine some thousands of feet deep, and in a matter of weeks, sufficient improvements in drilling space could easily be provided... It would not be difficult, Nuclear reactors could, heh... provide power almost indefinitely. Greenhouses could maintain plant life. Animals could be bred and slaughtered. A quick survey would have to be made of all the available mine sites in the country, but I would guess that dwelling space for several hundred thousands of our people could easily be provided. [Selecting who would go down] could easily be accomplished with a computer set and programmed to accept factors from youth, health, sexual fertility, intelligence, and a cross-section of necessary skills. Of course, it would be absolutely vital that our top government and military men be included to foster and impart the required principles of leadership and tradition.
Q: Wouldn't this nucleus of survivors be so grief-stricken and anguished that they'd, well, envy the dead and not want to go on living?
When they go down into the mine, everyone would still be alive. There would be no shocking memories, and the prevailing emotion will be one of nostalgia for those left behind, combined with a spirit of bold curiosity for the adventure ahead! Ahhh!
https://www.withouthotair.com/
Obviously there's no simple naive answer to your question, but essentially to a first approximation the answer is yes, it's possible. The changes we need to implement are pretty dramatic and some particular things don't look very viable (say, regular people making frequent international flights), but aside from those it's entirely doable and reasonably affordable. It's purely a matter of willpower.