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Yes, it's possible to disable past dates.
Please see this Calendar Widget here http://widgets.jotform.com/widget/date_reservation. It allows you to disable past dates. You can also specify how many dates can be chosen at a one time.
What about the option in the standard Jotform date-time field settings that says
"Disable Past Dates
If set yes users can not enter dates earlier than then."
I've tried setting this to "yes" but it doesn't seem to be working (I can still select dates in the past). Is that why you referred to the reservation widget instead?