I'd say that it depends on the audience for the site. If the site has existed in a previous form then see if it has some sort of analytics tracking so you can see what browsers were being used by the people who visited it.
At the very least put in a warning message letting people know that the site might be broken on older browsers and prompting them to upgrade. A quick example is this:
<!-- Prompt IE 7/6 users to upgrade to a newer browser. -->
<!--[if lt IE 8]>
<p class="chromeframe">You are using an <strong>outdated</strong> browser. In order to experience this website properly, please <a href="http://browsehappy.com/">upgrade your browser</a> or <a href="http://www.google.com/chromeframe/?redirect=true">activate Google Chrome Frame</a> to improve your experience.</p>
<![endif]-->