If you haven't seen it, http://docs.splunk.com/Documentation/Splunk/latest/Admin/Timesconf might be of use to you.
On the other hand, you can create an input that defines a token you can use as the values for
latest in the search string.
If you provide more detail or an example of what you're trying to do, we can provide a more effectives solution/recommendation.
The way I handled this recently was to forego the time picker and use a multi-select in concert with the automagic "date" field. Note: I've limited the date picker here to the last 15 days, so as not to overtax the SH. Adjust the parameter to meet your needs.
<input type="multiselect" token="DATE_tok" searchWhenChanged="true"> <label>Date</label> <choice value="*">Any</choice> <prefix>(</prefix> <suffix>)</suffix> <valuePrefix>date="</valuePrefix> <valueSuffix>"</valueSuffix> <delimiter> OR </delimiter> <fieldForLabel>date</fieldForLabel> <fieldForValue>date</fieldForValue> <search> <query>sourcetype="SplunkNinjaDataSource" | stats count by date</query> <earliest>-15d@h</earliest> <latest>now</latest> </search> </input>
Just add the token $DATE_tok$ into your search, and you're off to the races.
If you select same date in both textboxes , it is automatically equivalent to 1 day. i.e. if you are selecting 05/27/2015 in both text boxes, it actually means 05/27/2015 (00:00:00) to 05/27/2015 (24:00:00).
As of now, I think there are not any available parameters under timerangepicker module which can help us achieving this.