Hmm, you would need to grab the variables set by the search plugin, and plug them into the settings parameter in the shortcode/plugin.
For example:
$custom_settings = array(
'taxonomy' => 'value_from_search',
'tax_term' => 'value_from_search',
);
wpsp_display( 123, $custom_settings );It would require you to use PHP in order to grab those variables from the search plugin.