The weight that each item in an application carries varies from program to program--some look at GPA and test scores more while others could care less about numbers. I think what matters most is your personal statement.
Anyway, for two of my programs I asked a professor to write a letter for me, who I only had one class with, but received an A in. You don't have to know your professors inside and out in order for them to write a great letter: all you need is to have gotten an A in their class, met with them during office hours, and were an overall good student. If you did all three, you can ask pretty much any professor you want, with some precaution (you may want to ask someone in the field you're interested in to write you a letter, for example).
A good rule of thumb for finding letter writers is that if you know a professor is going to write you a weak letter, don't ask him/her. I've been in this position as well.
It doesn't hurt to ask, though. Really. I was nervous to ask said professor for a letter but she agreed, to my surprise. You can also ask employers for letters. Most MA programs require at least two letters to be from faculty members. The third can be an employer or somebody like that.
Hope I answered your question.