Can I setup a reminder email to remind me on the date, instead of x days before or after?

I just set up a quick test and using '0 days before the date in the field...' worked for me (at least when clicking 'send test email'. I would have to wait until tomorrow to fully test....). I would double check your reminder email, and if it still isn't sending, check with Customer Support.

If you want to test, just be sure to make a dummy record with todays date and put the 0 in and send a test email. Be sure to add a filter that ONLY sends your test record, or else every person with todays date will get the test email :)