Do you really have a column named "date"? If so, it's not a great practice. The only way I could get it to work was to do:
SQL> CREATE TABLE tt (ID integer, "DATE" DATE);
Table created
SQL> insert into tt values (1, null);
1 row inserted
SQL> update tt set "DATE" = sysdate where id = 1;
1 row updated
SQL> select * from tt;
ID DATE
------ ---------
1 14-Apr-11
SQL>