In your example, you're not using the date() function in PHP, but rather your SQL engine's DATE() function (if it has one).
If you're using MySQL, it doesn't have a function called DATE(). Try CURDATE().
I'm assuming you want to select all race_id's where the race's date is today or earlier. If you're trying to do something else, post more details.
By the way, I'm assiming your race.date field is a DATE field and not a DATE/TIME or TIMESTAMP field. If it is a TIMESTAMP, try using NOW() instead of CURDATE().
Hope this helps.
Rob