Missouri born, and I say that.* Never been to Pittsburgh, no family connection either. It seems a little more widespread than most people think, but still not too terribly common.
- Not during a job interview, though. Only after I get hired.
My Pittsburgh relatives (all of German ancestry, incidentally) would say, “The floor needs warshed.” But if you ask too many questions about it, you’re just being a nebbish.
I think it’s funny that you say that, because to me it’s without a doubt a dropped infinitive. I might say, “My car needs to be washed,” but more commonly I’d say it needs washed. (and boy, does it ever!) I would never think to say, “My car needs washing.” (and it does *not *need “warshing” - even I have my limits)
I did not know that dropping “to be” was incorrect until called out on it by a coworker when I was in my 20s. I can’t say I’ve quit doing it, either. The point gets across either way, no?
My wife does this, which leads me to occasionally pull my children aside and whisper corrections into their impressionable young ears. 
She was raised in Chicago, but may have have gotten this from her Southern Indiana parents. Southern Indiana has a strong German (and Amish) heritage in some areas.
I can tell you this construction is common in SE Pennsylvania, where I grew up, as well. I was saying it long before I moved to Pittsburgh.
I am also pleased to note that it is contagious; I have managed to infect my Norwegian husband and our two kids 
Wherever it started, it’s definitely spread. I used to use it when I was younger, in California, and I can’t swear that I’ve stopped. Although in high school I had a friend who hated that construction and would nearly tear her hair when she heard it. So I learned to suppress it, at least for awhile.
The same is very much in evidence here (Northern England) It is not at all uncommon for people to drop ‘to be’ and fail to substitute ‘-ing’.
I just sounds all wrong to me.