Wether or not it's going to affect usability depends on your audience, the device they're using, and what you've decided on for a minimum width.

Most smart phones allow you to scroll and zoom, so you may want to set your minimum width to whatever the lowest width is that won't hinder your content. However, the whole purpose of responsive design is to be able to change your layout at different widths, allowing you to fit content in. You should be able to find some layout solution for nearly all sizes, unless large images or charts are part of your content.

Either way, I generally don't worry too much about widths below 320px, and it seems neither do most web designers.

responsive website min-width?
in hibernate4.1.9 buildsessionfactory method is deprecated so why serviceRegistry is passed to buildsessionFactory
