Get posts by querying taxonomy and certain terms of the taxonomy?

The field parameter in the tax_query should be set to slug as it seems that you are passing the term slug. Any value passed to field except slug or name will cause the field parameter to default to term_id.

Always remember, the value passed to field should match the what is been passed to terms, so, if terms is term slugs, field should be slug

EDIT

Final solution from OP taken from comments

$args = array( 
    'post_type' => 'schedule', 
    'posts_per_page' => 15, 
    'tax_query' => array( 
        array( 
            'taxonomy' => 'schedule_day_taxonomy', 
            'field' => 'term_id', 
            'terms' => 1278 
        ) 
    )
);