If a country's leadership spends a significant portion of its country's wealth on a "this is absolutely worth destroying your daily lives because it will protect you from nukes" shield.... and that shield fails even once.... that country's leadership is turbo fucked. What will the citizens think?

Who cares. They don't live in a democracy. Firstly it wouldn't be spending a significant portion of the country's wealth. The US spent several trillion dollars on Afghanistan through Iraq wars over a decade, it can afford to spend trillions of dollars on this. Neither of those wars "worked" by the way and are understood to have ended in failure, yet the US government stands un-overthrown by people outraged by this because it just is accepted and if there were any outrage it could be brushed off as "Trump lied" as the waste of those wars is brushed off as "Bush lied". If you understand how the financing of empire works and the whole reserve currency thing (which it still stands to have for at least another decade IMO). I mean this is a "the people will rise up when denied healthcare and housing and seeing it spent on the military", uh no. Americans have been taking that for quite some time. They don't know, they don't care, it's too abstract.

Another point: they'd be triumphant that the shield worked at all and for the most part. Those still alive would be screamed at that the only reason they're still breathing is because of our wondrous shield and it's a shame it didn't save everyone but that was because of the evil (insert racist messaging) and the whole thing would be heavily massaged by propaganda.

Besides seeing how they reacted to 9/11 as long as the attacks are spun as aggression against the US and Americans most or enough anyways will lose their minds and turn into frothing monsters demanding we go over and literally eat the children of the survivors to punish those people even further for daring to hit us. Those unaffected will be raving maniacs, the dead will be canonized, the survivors will have quotes cherry picked and any who dare offer any nuance will be shoved away from the cameras as it ever has been.

What would the soldiery think about knowing their rations were cut, their equipment is falling apart, and the political/military leadership instigated agression against an enemy that can reach out and in a flash zero out 100k to 1,000k lives. Why would they have faith in their leadership, why would they fight for that?

What? Where is this coming from? Show your work. How do you arrive at this? None of that follows from this plan, this system, this idea. The soldiery would be triumphant that they wouldn't have to fight a war against a fully armed enemy and that they would be getting over to China to pillage, to plunder, to assault the population, to pluck their women for themselves, to have a cushy job getting to kill lesser humans and feel supremacist about it. The soldiers in the core would remain as they long have been which is compliant for free college, accepting of the poisoning at their training bases as it doesn't manifest for decades and happy to excuse their participation in the murder machinery of empire. I mean they have faith and fight for the clowns that run us now. It just seems a stretch.

This event would only happen once. And only need to happen once to secure capitalist hegemony and the new American century. They'd have to placate Russia a bit probably and the risk of a nuclear war between those two capitalist powers would be pretty great.

I point back again to 9/11. That is how Americans would react, with outrage that anyone dared hit them and kill Americans. 800 million dead Chinese wouldn't matter. Why the dead died would be ascribed to evil foreign powers and races as it was with 9/11. Those offering a critical narrative would be silenced, deplatformed, shouted down, and beaten. Eventually after 10 years some people might begin to re-evaluate it a bit but it wouldn't matter.

As to my scenario where they let through most of the nukes intentionally but shield strategic areas, I still don't hold out faith for Americans suddenly developing a conscious and class consciousness. They might accept a few patsies being frog-marched out on TV or in their area and visibly and openly executed or they might just accept that those responsible died in the blasts and we have to work together to build a new white supremacist state in memorial to the survivors. It also wouldn't matter if they did suddenly adopt socialism and killed those who'd carried out the plan as the NATO remnants in Europe would come over and squash them and carry on the grand capitalist crusade of subjugation of humankind. Most likely the survivors from such an attack wouldn't have accurate info and wouldn't in the immediate decade that follows be able to piece together what had happened and the scale of the crimes of the people who took them in and gave them food, water, and put them to work rebuilding.

The planners of empire and war need only believe this all to be true and not have reliable information otherwise to set it in motion and at that point it doesn't really matter if China hits them back harder than is acceptable for rebuilding because we're dead, China is dead, it's all a smoldering ruin.