jQuery UI's datepicker demo has some nice ways to deal with this situation. One is their "button bar" which allows you to have buttons with your datepicker, allowing you to add commands like "todays date" ect:
Example from JqueryUI
Note how the current date is also highlighted. Using two datepickers, like the date range in this example jQuery Datepicker, one for start date and one for end date, you can use the highlighted current day as an easy way to start/end a date range on "today". in addition you could add a button to one or more datepickers, like the below:
This allows quick access to set either calendar's date to the present date.
In addition if most searches are going to use today's date, you might just default to the current date and let users specify the end date only if they need to.