Charisma is incredibly important in this game. It's always one of the stats that I jack up at the beginning, regardless of the type of character I'm trying to build. I basically always carry a charisma boosting outfit with me as well. Reginald's Suit, a Trilby Hat, and the Black-Rim Glasses are good for an extra +5 charisma. It takes 11 charisma to pass all speech checks in the game, and 10 charisma will pass the vast majority of them. Unless you've invested virtually no points into charisma, that +5 will help you pass basically any speech check in the game.
Really though, even if you don't have a charisma suit with you all you have to do is just quicksave before selecting the dialog. If you fail it, reload until you pass it. Eventually you will.
I passed the speech checks and spared Danse.
I couldn't agree more. I've made this same comment on several occasions. I really feel like the voicing behind Elder Maxson is some of the most well done dialog in the entire game, and this speech is probably the best example of it. Maxson almost, but not quite makes me sympathize with his position and question whether or not I'm doing the right thing by sparing Danse. This speech really just shows how steadfast Maxson is in his beliefs and convictions, and it's really quite moving. Even though I didn't agree with him that Danse needed to be killed, it motivated me to continue on with the BoS ending that I was working toward.