Well… your bullet doesn't have to be silver as long as you hit a vital spot.
Sadly, there isn't one. There's an awful lot of people who are unable to visualize design (thankfully, otherwise we'd all be wearing foam hot-dog suits for a living), which is why they come to us. A few points you should try to make:
1) "I'm the expert, and you would be wasting your money if you didn't give my (professional, experienced) judgement the weight it deserves". These folks wouldn't even blink if a plumber told them that the pulse modulator in the secondary warp coil in their bathroom toilet had broken loose and would have to be re-aligned (no - really. I worked as a plumber in college). So why are they arguing with you? Obviously, "You're a stupid doo-doo head who should let me do the job you're paying me to do" isn't the most diplomatic phrasing. But point out that they are paying good money for a product (and it's not necessarily the document / web site they end up with - it's the design judgement and aesthetic sense you bring to the table).
2) Give them a mockup that purposely shows why that white space is important. Tell them: "Most people won't read past the second sentence - your message is too important to get lost in a sea of text" (yes, I know - sometimes shameless ego massage is needed. You can always scrub yourself clean later). Ask them to spend 15 seconds reading the page and to mark where they stopped. Show them how the important parts get lost in a sea of text and remind them that most of the world's attitude toward the written word seems to be "TL;DR". I sent my boss the study that showed the eye tracking pattern for web sites to convince him that "less is better".
3) In the end, you may have to give up. After all, they're paying for it. But if it's a design that completely horrifies you there are a couple of things you should do. First and foremost, keep a copy of any and all dialog (including phone calls, even if it's only a quick series of notes with a time a date stamp). That way, when everyone keeps telling your client that their web site is hard to read you'll have something to use as a backstop. Also, make it clear that you will not be placing your name or reputation anywhere on this web site (even if you don't regularly do it). Again, some diplomatic language is probably best, but if you don't believe in the design you shouldn't have to take the credit (or blame) for it.