I do not know about Churchill but I do know of the American perspective. Many high officials believe the invasion would be god near impossible because of the high casualty mark. The Japanese soilders at Okinawa would never surrender they would die fighting for what they believed in honor and their emperor. In battle they would fight rigorously and eventually when they ran out of supplies they would BONZAI charge with their bayonets either killing all of them or resulting in a victory with high casualities. Of course this method was flawed but the Americans knew that the Japanese would never surrender or at least easily. If they did even then many would commit suside and only a measly up to like 3000 would actually surrender. If one was to atack the mainland this type of fighting would surely have amplified as the attack on the mainland would surely have unified. The Japanese spirit was to win, to have honor, and if victory was not attained then attack the enemey until we all die in honor and at least we took them down with us. General Macarthur estimatated originally 1-3 million dead and later he would esimate 3- upwards to 8 million. Even more he estimated that we would need millions of troops to even invade. The Japanese would never give up. If you never herd of the story one such story can truly embody this even after the war when Hiroo Onada a Japanese soilder did not surrender until 1974. He countinued to fight in the Phillipines until they ulitamatley found the man and captured him on his guieralla attacks. If just 10% the soilders had this kind of determination then millions of men were surely to die on both sides. That's why the US planed to Nuke the Japanese as it would force the Emperor to make a decision of the death of hundreds of thousands of his own people not in battle or continue the fight until everyone would die in battle. Of course that is the extreme for the Emperor so he surrendered fearing the end of his empire and the people as soilders were in dismay and so even then they attempted a coup for power so they may continued the War. If a war on the scale you have mentioned were to occur ever man, woman, and child would fight until the very end and ulitamtley that would be extremly costly. Sorry for all the incorrect grammar.
