Can WordPress handle a big website?

Yes. In fact WordPress is used by companies like The New York Times, CNN, Forbes, eBay, GM and many other large companies. WordPress is robust enough to handle virtually any size website.

What is WordPress?

WordPress is open source web software that you can install on your web server to create your website, blog, community or network. WordPress started out as a tool for blogging, but has evolved into a full-fledged Content Management System (CMS), capable of powering websites, networks and communities.*

*Source: WordPress.org