You pretty much get what you pay for. One of my first media buy campaigns, I was on a really tight budget at the time and settled with some cheap $2/mo hosting. The campaign blew up and eventually I ran out of bandwidth in a few days and had to upgrade.
In another case, I had an SEO campaign I was playing around with, but since it was adult I decided to put it on my hostgator server. I'm an SEO noob, but the site starting ranking pretty quickly and I started seeing leads on a daily basis. A few weeks later, I never realized but hostgator kicked me off that server for using too many resources. Those leads ended up turning into sales weeks later and I still get checks in the mail for that campaign (lifetime revshare). Had I shelled out a few more bucks, those checks would've been 3 - 4x bigger right now.
Cheap hosting is fine if you're just starting out and don't have the budget, but ALWAYS upgrade whenever you decide to start taking your projects more seriously.