If you are working with dates, like it seems you are saying :
Where start would be a DATETIME field
with data like 2009-09-23 11:34:00 and
$date would be something like
2009-09-23
Using LIKE might not be the only/best solution : there are functions that deal with dates ; and you probably can use comparison operators too.
In your case, you can probably use something like this :
select *
from headers_sites
where date_fetch >= '2009-07-15'
limit 0, 10
Of course, you'll have to adapt this query to your tables/fields ; something like this might do, I suppose :
SELECT * FROM schedule_items WHERE start >= '$date'
This will get you every data for which the date is more recent than $date.
If you only want the date of one day, this could do :
SELECT *
FROM schedule_items
WHERE start >= '$date'
and start < adddate('$date', interval 1 day)
This might be better than "like", if you start column has an index -- not sure, though ; but, still, what you are willing to get will be obvious from your query... And that is nice.