Brad, you're referencing Structure:Entries (http://buildwithstructure.com/tags#tag_entries) NOT structure_entries (http://devot-ee.com/add-ons/structure-entries) which some of the answers and comments are referring to.
Assuming it is the Structure native tag, then the documentation only states it supports the same variables as a channel tag - not that it supports the structure:nav parameters.
Your reference to the existing code:
{exp:structure:entries channel="portfolio" parent_id="{structure:page:entry_id}" disable="categories|category_fields|member_fields|pagination"}
Would mean that structure:entries tag would ignore channel
and disable
and they do nothing.
So the parameter isn't supported, possibly email Structure support to request they include in a future version?
Solution... (warning hack alert)
"hidden" (hidden from nav) is a column in the structure table (with a row for each page). The structure:entries tag takes the parameter parent_id and calls a function called get_child_entries passing the parent ID. This function does the SQL query and has it hard coded in to ignore any entry set to hidden.
2 solutions (the quick way):
modify lines 1115 - 1120 of sql.structure.php (v3.3.10)
$this->EE->db->select('entry_id')->from('structure')->where(array(
'parent_id' => $parent_id,
'entry_id !=' => 0,
'hidden !=' => 'y',
'site_id' => $this->site_id
))->order_by('lft', 'asc');
Change to:
$this->EE->db->select('entry_id')->from('structure')->where(array(
'parent_id' => $parent_id,
'entry_id !=' => 0,
'site_id' => $this->site_id
))->order_by('lft', 'asc');
Removing the hidden reference in the WHERE clause. Downside this will change ALL calls to {exp:structure:entries}
.
Alternative solution:
Add the parameter for override_hidden_state in the entries function (starts from line 111 in mod.structure.php) and pass it to get_child_entries as a second parameter. In get_child_entries (from line 1110 in sql.struture.php) add the extra parameter (giving it a default value of "n" to ensure all existing calls continue to work) an modify the SQL call to reflect the choice of showing hidden or not. I've not gone into the exact code examples as I expect the 1st solution would be suitable for most people and you've already solved the issue via custom SQL.