[namelessoracle]

My experience dealing with product managers is you have to phrase it one of 2 ways.

If you know your taking technical debt, explain to them that its like a credit card, but instead of money its time, and we can go ahead and swipe it, but you will eventually have to pay it with interest, and the cost you are paying is every future story is gonna be a little bit slower until things that should be able to get done in a week take a month. ( I have seen this happen personally with a project and the whole thing had to get completely rewritten)

If its unforeseen technical debt, dont call it that. Call it foundational work. Tell them the foundations were not set in a way to support X or Y feature so we need to change/update the foundations to get them the feature they want. This seems to work best. Don't even tell them there is a hack or duct tape solution, bring up the foundational piece first. If business needs has a requirement that it gets out faster, then transition to the credit card analogy and explain they are now swiping the credit card and whenever they complain about velocity use this an example.

The biggest problem is that product managers typically move on or get promoted by the time the technical debt they incurred causes bankruptcy. And fixing that usually tends to involve a rewrite which will have new flavors of technical debt (especially when its in new language), with a new product manager selling their "V2 solution" as so much better. (and successful delivery of that seems to involve them getting promoted or moving to another place soon after)