Clear link should clear the time, not just the date

When selecting a date using the JS popup date selector, clicking Clear will only clear the date. I cannot think of any possible use case where one would want to clear the date but would not want to clear the time. Thus, a user clears the date, tries to submit the form, the date field doesn't validate because the time field hasn't been cleared. This could be very confusing to some users, and it also makes them spend some extra time to clear the time field. And clearing the time field isn't exactly intuitive either; only the Delete key and not the more widely used Backspace key will clear the time field.