NULL becomes default

A surrogate key has been introduced on a table with modifiers:

Column | Type |
Modifiers
-------------+-----------------------------+------------------------------------------------------------
new_id | integer | not null default
nextval(('some_id_seq'::text)::regclass)

However, some legacy software inserts into the table by first getting column
names and then composing an INSERT for all the columns, filling in any
undefined values with NULLs.

Thus when it attempts to insert a row I get a:

ERROR: null value in column "new_id" violates not-null constraint

Thus I would like NULLs in such INSERTs to be treated as DEFAULT rather than
violating the constraint. Is there an easy way to do that at the database
level?

Thanks

Julian