Try running the following:

$ MAILMAN_EXTRA_TESTING_CFG=/home/barry/projects/mailman/postgres.cfg tox -e pg

where you replace the path to the postgres.cfg with one of your own as described in src/mailman/docs/START.rst

Pretty quickly we hit an exception:

======================================================================
ERROR: LayerSuite
----------------------------------------------------------------------
Traceback (most recent call last):
  File "/home/barry/projects/mailman/trunk/.tox/pg/lib/python3.4/site-packages/sqlalchemy/engine/base.py", line 1139, in _execute_context
    context)
  File "/home/barry/projects/mailman/trunk/.tox/pg/lib/python3.4/site-packages/sqlalchemy/engine/default.py", line 442, in do_execute
    cursor.execute(statement, parameters)
psycopg2.ProgrammingError: column "id" does not exist
LINE 1: ...LECT setval('"domain_owner_id_seq"', coalesce(max("id"), 1),
                                                             ^


The above exception was the direct cause of the following exception:

Traceback (most recent call last):
  File "/home/barry/projects/mailman/trunk/src/mailman/testing/layers.py", line 207, in testTearDown
    reset_the_world()
  File "/home/barry/projects/mailman/trunk/src/mailman/testing/helpers.py", line 476, in reset_the_world
    config.db._reset()
  File "/home/barry/projects/mailman/trunk/src/mailman/database/factory.py", line 123, in _reset
    self._post_reset(self.store)
  File "/home/barry/projects/mailman/trunk/src/mailman/database/postgresql.py", line 49, in _post_reset
    """.format(table))
  File "/home/barry/projects/mailman/trunk/.tox/pg/lib/python3.4/site-packages/sqlalchemy/orm/session.py", line 1023, in execute
    bind, close_with_result=True).execute(clause, params or {})
  File "/home/barry/projects/mailman/trunk/.tox/pg/lib/python3.4/site-packages/sqlalchemy/engine/base.py", line 914, in execute
    return meth(self, multiparams, params)
  File "/home/barry/projects/mailman/trunk/.tox/pg/lib/python3.4/site-packages/sqlalchemy/sql/elements.py", line 323, in _execute_on_connection
    return connection._execute_clauseelement(self, multiparams, params)
  File "/home/barry/projects/mailman/trunk/.tox/pg/lib/python3.4/site-packages/sqlalchemy/engine/base.py", line 1010, in _execute_clauseelement
    compiled_sql, distilled_params
  File "/home/barry/projects/mailman/trunk/.tox/pg/lib/python3.4/site-packages/sqlalchemy/engine/base.py", line 1146, in _execute_context
    context)
  File "/home/barry/projects/mailman/trunk/.tox/pg/lib/python3.4/site-packages/sqlalchemy/engine/base.py", line 1332, in _handle_dbapi_exception
    exc_info
  File "/home/barry/projects/mailman/trunk/.tox/pg/lib/python3.4/site-packages/sqlalchemy/util/compat.py", line 188, in raise_from_cause
    reraise(type(exception), exception, tb=exc_tb, cause=exc_value)
  File "/home/barry/projects/mailman/trunk/.tox/pg/lib/python3.4/site-packages/sqlalchemy/util/compat.py", line 181, in reraise
    raise value.with_traceback(tb)
  File "/home/barry/projects/mailman/trunk/.tox/pg/lib/python3.4/site-packages/sqlalchemy/engine/base.py", line 1139, in _execute_context
    context)
  File "/home/barry/projects/mailman/trunk/.tox/pg/lib/python3.4/site-packages/sqlalchemy/engine/default.py", line 442, in do_execute
    cursor.execute(statement, parameters)
sqlalchemy.exc.ProgrammingError: (psycopg2.ProgrammingError) column "id" does not exist
LINE 1: ...LECT setval('"domain_owner_id_seq"', coalesce(max("id"), 1),
                                                             ^
 [SQL: '                SELECT setval(\'"domain_owner_id_seq"\', coalesce(max("id"), 1),\n                              max("id") IS NOT null)\n                       FROM "domain_owner";\n                ']


The domain_owner table does not have an id column.  The workflowstate table doesn't either, but adding it to the latter causes other problems.   Clearly we are not ready for PG.