It's like Gandhi said when asked if his tactic would work with someone like Hitler. He said, "It would be difficult." But I think there's a fair argument that the answer really is "No." Sadly, I don't think what you are trying to do can be done. It's not that I'm trying to be pessimistic, but rather I'm trying to be honest.
The problem to me is not that managers need convincing. The better ones already understand that debt can be a killer if not managed. But whether they understand it or not, whether they're good managers or bad, they all face the pressure to deliver, and that delivery is judged by their bosses against a date. Quality only matters if it's extremely bad, in which case it's the developers' fault, or extremely good, in which case it's management brilliance that made it happen. Quality just needs to be "good enough."
I think I like what Renesis said in his answer, because it's one of the few that understands that management thinks very differently than engineering. And I think we've all seen the progression of companies to become date-driven and more project-managed as opposed to customer and quality focused. By this, I mean typical companies, not the really stalwart ones that have the guts to say "It'll be done when it's done" (like Apple Computer or id Software - and yes, I understand that sometimes people aren't at liberty to take that approach).
But here's the thing: companies that take the quality-first approach...what do you notice about them? That's right, they're run by engineers, not salesmen, marketers, project managers or accountants. Think of HP, Apple, id, Google, Microsoft, and IBM. All started and made successful by engineers, not salesmen, though salesmen certainly played a part, and I'm sure many would debate having Microsoft associated to quality :). And of those, the ones that went downhill got away from engineering-driven leadership. There's a whole host of arguments in that statement though, as there are plenty of technical companies that ultimately failed due to an inability to adapt to changing times and manage their own growth. I don't see engineering-based leadership as the cause for those failures, to me that's an issue of skills and business acumen that are independent of someone being a developer or an accountant. I think generally speaking, however, that there is a dedication in engineering to the rigors of accountability and discipline that benefits companies where engineering is a component.
Seriously, look around. IT leadership is sorely lacking. Focus is always on cost and time, and rarely on quality as long as it's good enough. IT leaders rarely report to the CEO anymore, now it's always the CFO. IT is stuck doing production support and increasingly beholden to project managers whose focus is on smaller, more digestible, and measurable chunks, not significant changes of revolutionary value (not that this is necessarily wrong; divide and conquer is a good thing, but the vision needs to be there for the big picture).
Sorry to take so long on this post, but in the end I think your question, about how to make management care about technical debt, is often better solved by finding the right leader, rather than changing the existing one. Explaining technical debt to standard thinkers means changing the focus to money and cost, as Renesis said, and I think that loses a lot in translation; even if you were successful at it, it would only matter if the top leader in the company bought it. Convincing your middle manager to do the right thing will probably only get him fired.
