Have a look at Brian's excellent answer to a similar question:
http://splunk-base.splunk.com/answers/7424/one-timerangepicker-for-all-charts-modules
Edit: and one answer from me to a similar question as well.
http://splunk-base.splunk.com/answers/12787/dynamic-dashboard-time-range-span-and-others
Yes exactly withput the need to run the searches again.
You can set a relative time from the search app. You could set it to only include results from the last month. Look to the right of the search bar.
Could you clarify this a bit - do you want a dashboard showing the data for some chosen day in the past? So like a timerange picker for choosing which day to show would do?