Is it possible to have a single date exposed filter with date range?
yes, there is a module for that, views_between_dates_filter, from module:

This Views filter provides the between date functionality you've been looking for by answering the question: &quot;What events are on this date?&quot; It displays all content (comparing start and end dates) occurring on a specified date.
It compares two date fields with one supplied date. Effectively it is the opposite of the standard Date Views &quot;between&quot; operator, which compares one date field with two supplied dates.