Wishes in the Present

Present wishes indicate something that is "contrary to fact." That is, wishes are something that is untrue but desired. 

For example,
I wish that I had a sports car. (The truth is I don't have a sports car.)
I wish that I were a doctor. (I'm really not a doctor.)

For present wishes, the past tense is used in the that clause, because it indicates a situation that is only imagined. Sometimes the word that is omitted.
For example:
She wishes (that) she had a diamond ring.
He wishes (that) he were rich.

To express possibility (can) and future intention (will), use the modals could and would respectively.
She wishes that she could sing.
They wish that she would stop.

When a "be" verb is required, the word were is used, regardless of the subject.
We wish you were here.
I wish (that) I were taller.

Mary is sick, she wishes she weren't sick, she wishes she were healthier.