This is not possible today. It would require a very short interval for the cronjob, and not all providers allows this.
If a SMS would be fine, then you could post a suggestion that there could be a minutes setting for the SMS. Then, when the cronjob that runs at night meet an event that is scheduled at the same day and marked for SMS - then there is sent an SMS with a specified time for sending ( xx minutes before the event takes place ) . Then the SMS provider will take over and the provider will send the SMS at the specified time. This way you could have a reminder close to the time for the event.
Or maybe a special cronjob that should run very very often and look for events to be sent as reminders ( sms and/or mail). There should be some logic that checks that an event is sent close to the start-time for the event - and only once.
I think you should post a suggestion for this, as it could be a useful feature. As I remember it has been discussed before, but I think it is a tricky one, and it should not bring problems in the existing mail/sms functions.
Make a suggestion and then it could be discussed - I think.