Something like this:
WHERE (subj_title.date - INTERVAL 2 DAY) <= '$date' AND (subj_title.date + INTERVAL 1 DAY) >= '$date'
There may be a cleaner query than this, but this should give you what you want. This might be a little cleaner:
WHERE subj_title.date BETWEEN ('$date' - INTERVAL 1 DAY) AND ('$date' + INTERVAL 2 DAY)
edit: something I just realized -- change it to 'INTERVAL 1 DAY' if it's a 'DATE' datatype, keep it '2 DAY' if it's a 'DATETIME' datatype.