JotForm is a free online form builder which helps you create online forms without writing a single line of code. No sign-up required.
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To confirm, you would like to disable a future date? That should be possible by using the "Limit Dates" option, you can refer to this guide: http://www.jotform.com/help/337-How-to-Use-the-Limit-Dates-feature-in-a-DateTime-field.
Let us know if that's what you are looking for.
Sorry what I meant to say was is there a way for an entire form to be made 'disable' at a given time in the future.
The feature to Disable Form on future date is available as well.
You can set the Expiration Date on the form so that it becomes unavailable/disabled on the specified date.
Follow this user guide on how to setup :
Let us know if this will still not work for you.