I don't know, that mindset is so foreign to me. If someone was overestimating how long it would take because they were simply trying to be conservative and not run into unexpected cost overruns, I would commend them. I've always considered it more prudent to expect something to take longer so you know the kind of budget you need up front instead of lying to yourself about it. It costs a lot more (in terms of lost time and productivity) to have to swing a new budget mid-project because it turns out you've burned through the planned budget and you're only 2/3 the way done with the project.

So, screw your manager, you're doing the right thing, in my eyes. I guess that's why I'm not in charge of anything.