Due to issues with lack of control on date/time formatting with native
browser date items, I am re-opening this as we have to fallback to 
text inputs in many cases.

Adding a javascript change handler of the text input for a date/time
that updates the date part of the popup calendar link might solve this.
That way editing or using the calendar to change the input will result
in the link starting with the current date.

See the datecopy.js in the tracker templates for a framework for
delegated event handling.