Hi Thomas,
Perhaps using the Auto Populate feature under the Layout Options -> Search box layout panel might help you: http://i.imgur.com/4eYXEX2.png
It’s a feature to display results initially on page load, where you can set a different limit from the default one. I’m not sure if this is what you are looking for though.
I would not recommend changing the script for this purpose though, there might be a better way to get around it. There are filters available to change the search phrase and the results via PHP, that might be a better option. Let me know if the auto populate is not working out, and I will look into it.