Just about everything Jefferson Smith say's during the filibuster is awesome. Quoting the Declaration of Independence helps a lot.
Even Senator Monroe, the senator whose had it in for Jeff, comes to admire him.
Monroe: Joe, I've never like this boy from the beginning, but nobody who isn't sincere wouldn't last this long, even against these impossible odds.
The visit to the Lincoln Memorial was pretty awesome. Also counts as a moment of heartwarming.
Jeff's on his last leg, but he never caves in.
Jeff; You think I'm licked. You all think I'm licked. Well, I'm not licked, and I'm gonna stay right here and fight for this lost cause, even if this room gets filled with lies like these!
Then after Jeff collapses during his filibuster a shot is heard. Paine actually tries to commit suicide!
Paine: I'm not fit to be a Senator. I'm not fit to live. Expel me! Expel me! Not him. Every word that boy said is the truth! Every word about Taylor and me and graft and the rotten political corruption of our state. Every word of it is true. I'm not fit for office! I'm not fit for any place of honor or trust. Expel me!