I finally figured out what the View's Argument Handling Code block is for. Here is a trick to use the same view to get both the all time popular content, and the recent popular content:

if( $args[1] == 'today' ) {

  $view->sort[0]['field'] = 'node_counter.daycount';

  $view->sort[0]['id'] = 'node_counter.daycount';

  $view->argument[0]['title'] = "Today's Popular Items: %1";

}

return $args;