The Forecast view only shows tasks which either start or are due on the displayed date. So, if you need it to appear for more than one day, the path of least resistance is to bump the start date along each evening if you haven't yet completed the task. When you knock off work for the day on 11/10, you look at your list of starting tasks for 11/10 and adjust their start dates to 11/11. I'm assuming that these are not multi-day tasks that repeat; in that situation a little more fiddling about would be required as the start dates set on the action when you complete it will be used to compute the start date for the next instance, and that's probably not going to give you the desired answer unless you completed the task the first day it appeared. I do have an Applescript that allows you to reschedule a repeating task without affecting the scheduling of the repeats in this thread:
http://forums.omnigroup.com/showthread.php?t=22073
On the Mac, you want to use the grouping and sorting options in context mode. Group by start, sort by due, availability remaining actions, any status is very similar to the starting portion of the Forecast view, and group by due, sort by due, availability remaining actions, status due soon is very similar to the due portion of Forecast view. If you want, collapse the groups showing dates that don't interest you, and save as a perspective with the Restore Expansion box ticked in the Show Perspectives window.