I'm going to second Robert S's answer, and expand a bit.
If you take the time, from the initial concept forward, to be standards-compliant and emit clean XHTML with CSS, you'll save yourself the majority of the pain. You'll probably be fairly close to your intended output across all the browsers right out of the gate. Sure, there will be some pixel-level wonkiness due to the way the box model is implemented, but you'll probably be "close enough" that no extra expense is needed.
I wouldn't go so far as to intentionally "tweak" my site to be sure it works with every browser -- not only is that expensive (in terms of time), but it's also doomed to fail as browsers come closer and closer to clean support for the standards.
FWIW, Chrome is a browser you absolutely should test with. As others have mentioned, it's based on Apple's WebKit. Testing Chrome and the Windows version of Safari will give you a very good handle on your site's user experience on the Mac platform, at least if you don't have a Mac available for testing. :)