I would do this by creating a Parameter Map that is based on a Query Subject that returns values of a number of significant dates eg. Today, Yesterday, Tomorrow, Last Year Today, etc...
Then, I would use the value of the appropriate date I need retrieved as a macro as the filter in my Query Subject.
So a query subject with following SQL would be basis for the Parameter Map (shows Todays Date as a number only):
SELECT
'TODAY_TY' as PARM,
to_number(to_char(a.CAL_DT, 'yyyymmdd')) as VALUE
FROM
[EDW].CAL_DT a
WHERE
a.CAL_DT = current_date
Then, once you've completed your Parameter setup, you would add the filter [relational_db].[QUERY_SUBJECT_NAME].[MY_KEY] >= #$[Your Parameter Name]{'TODAY_TY'}# to your query subject.
This should not time-out as it passes the value of the date rather than the calculation of the date which will be performed against every row you are comparing against.
Hope this helps,
Adam