Using post title as term in query, only working with single word titles

Question

The term needs the slug of the term, not the human read description so “hello-world” not “Hello World”

Try using the sanitize_title function:
http://codex.wordpress.org/Function_Reference/sanitize_title

Also, add an else case for your loop to catch the ‘no posts found’ case, etc, when you have an issue it’s a good idea to have as much information as possible.

Additionally:

    'taxonomy' => 'suppliersTax',
    'term' => $supplier,

can also be written as:

    'suppliersTax' => $supplier,

edit: the most verbose definitive precise flexible method of writing it is this:

'tax_query' => array(
    array(
        'taxonomy' => 'supplier',
        'field' => 'slug',
        'terms' => sanitize_title($supplier)
    )
)

as seen here: http://codex.wordpress.org/Class_Reference/WP_Query#Taxonomy_Parameters

Also looking at your code in your comment you use:

$homeSOTMHeader = get_posts( $args );

foreach( $homeSOTMHeader as $post ) :   setup_postdata($post);
?>
    // stuff
<?php endforeach;?>
<?php wp_reset_postdata(); ?>

It would be clearer to use this instead:

$q = new WP_Query($args);
if($q->have_posts()){
    while($q->have_posts()){
        $q->the_post();
        // stuff
    }
} else {
    ?><p>No Posts were found</p><?php // important information to have for debugging purposes
}
wp_reset_postdata();