Postgres ignoring clustered index on date query

I have a large table that I run queries like select date_att > date '2001-01-01' on regularly. I'm trying to increase the speed of these queries by clustering the table on date_att, but when I run those queries through explain analyze it still chooses to sequentially scan the table, even on queries as simple as SELECT date_att from table where date_att > date '2001-01-01'. Why is this the case? I understand that since the query returns a large portion of the table, the optimizer will ignore the index, but since the table is clustered by that attribute, shouldn't it be able to really quickly binary search through the table to the point where date > '2001-01-01' and return all results after that? This query still takes as much time as without the clustering.