What does " I can't do Thursday" mean?
If while arranging a meeting a person says "I can't do Thursday", does it mean " I can't meet you on Thursday"?

Question

What  does " I can't do Thursday" mean?
If while arranging a meeting a person says "I can't do Thursday", does it mean " I can't meet you on Thursday"?

Answer

It is an American expression. 
Americans 'think' that they speak English, but they frequently do unusual things to English grammar. 
It means - I am unable to meet you on Thursday.
Other English speakers would say -
I am unavailable on Thursday.
I am not able to meet you on Thursday.

Answer

Yes. I can't do tomorrow. I can't do next Friday. I can't do lunch. Etc.

Answer

Thank you. Is it a common phrase?

Answer

Yes, that is exactly right! :)