It's possible to set the StopPublish date when creating a new page se snippet below, so It should be possible to do what you want if you set the date on the publish event.

See this blogpost on how to easy jack into the EPiServer events: http://talk.alfnilsson.se/2013/03/17/simplifying-event-handling-in-episerver-7-cms/ 

Set default date when creating new page:

public override void SetDefaultValues(ContentType contentType)
{
base.SetDefaultValues(contentType);
StopPublish = "Your new date";
}

You can do what Per said or you can hook into the publish event and set the stop publish date there as well.  Either one will work.  If you don't want to do it at the model level and want to have more conditions before setting it, I would suggest the publishing event.