What does it mean when Tom says: "When the s**t hits the fan I’ll be right behind you" in That Championship Game by Jason Miller? Is he going to support or George or not?
What does it mean when Coach said "walk softly and carry a big stick"? Another reason for the change from Roosevelt's "speak softly and carry a big stick"?
That Championship Game is a Pulitzer Prize-winning play by Jason Miller. It is set in 1972 and recounts the reunion of some former players and their coach, twenty years after winning a championship basketball game.
One major player in the story is the old-fashioned and patriarchal Coach, who is stuck in prejudicial, 1950s thinking and unreasonably expects the unquestioning loyalty of his former players. The other four characters are Coach’s former players. Phil is rich and immoral. He is bored and regularly has affairs (with his wife’s approval). He was responsible for getting another teammate, George, elected mayor in the last election, and he benefited financially from that act.
James is a junior high school principal with political aspirations; he was George’s campaign manager in the last election. James is bitter and believes he is consistently gets last consideration in everything—and he is probably right. Tom is James’s alcoholic younger brother, and he is a wastrel in nearly every way. Despite his dissipated condition, he is arguably the most realistic of them all.
The first quote you mention is spoken by Tom early in the play, right after James and the others bring back some beer and food; Tom speaks the line in response to his brother’s comment:
Phil: How are you doin’? Stay sober. I may need you tonight.
Tom: When the shit hits the fan I’ll be right behind you.
The context of this line has nothing to do with supporting or not supporting George in his bid for re-election. In fact, the line which follows the “fan” line is this:
James: You can handle this stuff [beer] in moderation. You can handle anything in moderation.
The phrase is a colorful one, and the image is vivid. Imagine literal “shit” hitting a fan; Tom says that when that happens, he will be right behind his older brother—not a position of sacrifice or support. As always, Tom is worried about himself and is perfectly willing to let someone else take the worst of whatever is happening. A paraphrase might sound something like this: when things get difficult, I’ll let you take all the grief and problems, and I’ll be standing safely behind you.
In terms of supporting George, Tom is planning to leave town after this little reunion, so he is obviously not particularly interested in supporting anything here. As a realist, he knows that George probably cannot win, even with Phil's reluctant help.
As for Coach's version of FDR's famous saying, he says that in answer to James's question about how Coach manages to stay so fit after so many years. Coach brags that, at age sixty, he can still take on all four of these much younger players in a game of basketball, weighs a trim 185 pounds, does ten quick push-ups, and has a tight, firm belly.
James: What's the secret?
Coach: "Walk softly and carry a big stick."
Then Coach changes the subject, without any further explanation.
We learn, through the course of the play, that Coach is a man who lives by his own set of rules and principles, regardless of their acceptability or morality. He expects unquestioning loyalty from all of his former players, demands that they forgive marital infidelity if it benefits him, and is not above ordering a player to deliberately hurt an opponent in order to win a game. He is an old-school thinker who lives and plays by his own rules. In the case of this quote, it is obvious he appropriated the quote for his own use and made it say what he wanted in order to apply to him.