How do I make my homepage slideshow to fit the page width?
Is your website wider than 960px ? ... I have you looked at online CSS tutorials such as Full Screen Background Image Pure CSS Code, or CSS3 cover property for background-images as mentioned here. I think the CSS Only Technique #1 is more what your looking for in your slideshow's inline images.

Anyways, Google will help you alot here. Views Slideshow ships with basic useable CSS, but it's not themed for everyones needs. It's up to you to tweak its CSS as you need. As an example I've previously given here -- taking a Views slideshow and using only css + jquery and changing it to meet client needs.

Sorry I dont know of a module that just does all the themeing for you, views slideshow does do 99% of the work for you by providing a workable slideshow for your site.