No. When you say to people, "That's the spirit," you're telling them they have a great attitude.
Examples:
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You: "Can you fix my car today?"
Your friend: "No problem! I'll have it running better than ever in half an hour."
You: "That's the spirit!"
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Your boss: "We have a big deadline. Can you work late tonight?
You: "Absolutely. This is a great project, and I'm going to do whatever it takes to get it done. You can count on me!"
Your boss: "That's the spirit!"
[I'm a copy editor and have tutored university writing.]