That *did* happen to me. I owed the IRS $40,000 on taxes where I hadn't even made $40k in my life thus far. It was for taxes when I was working as a freelancer right out of college and was making less than $16,000 per year, and living out of my parents house.
I could not get it settled with them until I refinanced my mortgage 10 years later and added what I owed on my mortgage to what I owed the IRS and essentially folded that debt into the mortgage. While it worked out for me in the end because I was able to sell my condo at the height of the real-estate boom, it still smarts that I owed the IRS more than I ever made during that period.