Edit: /components/com_search/search.php

At the top of the file around line 20 it should look like:

// page title
$mainframe->setPageTitle( _SEARCH_TITLE );

Right after that add:

// all words default (modded by yourname)
  if($_REQUEST['searchphrase']=='') {
  $_REQUEST['searchphrase']=$_GET['searchphrase']='all';
  }