If the wordpress blog isn't heavily loaded down with lots of plugins and your hosting your wordpress blog on a shared server that isn't oversold then a good web host can likely handle 3,000 daily unique visitors with ease.
If you're hosting that same blog on an oversold host like Hostgator that is owned by EIG then your website will likely crash with less visitors.
It totally depends on how many plugins if any you have on your wordpress blog and whether you host videos on your own blog or have the videos hosted on another web server and if you're on a good shared host server with a good shared hosting company.
Most shared hosting that is quality hosting can likely handle 3,000 daily unique visitors with ease while others can't cope.
Check out http://webmasterbabble.com
and look in the advertising section for good quality web hosts and ask for reviews on the web hosting companies on that forum.