"This guy I've been talking to hasn't responded to me in two days. He warned me he would be busy with lots of work and school. Should I text him that at this point I'm pretty much done or should I give him the benefit of the doubt because he warned me?"
So, it sounds like this has been going on for a while now. At this point, it's obvious that he's just not that interested. He doesn't like talking to you, he's not that interested in getting to know you or he's with someone else. Because no one is that busy. Two fucking days? Unless he's in outer space somewhere working, no one is that busy.
Here's the thing: Everyday we all do something that we don't necessarily have to do. For instance, every morning before we go to work, we get ready. We get ready by fixing our hair, putting on makeup if you're a woman, shaving if you're a man, etc. We do these things because we want to look presentable. But we take the time, we make the time. We find the time to do these things.
If he can't find two minutes to text you, "Good morning. How are you doing?" ... Everything good? ... Okay, Good, I'll talk to you later." If he can't spare those two minutes, then he's just not that interested in you.
When he's walking to school, he can text you. When he's taking a shit, he can text you. If he's in an elevator, he can text you. If he's waiting in line for something, he can text you. But he's not interested in doing those things, because again, he's not interested in you.
Now, there are people who will bring up the whole, "Oh, you're just being needy." Get out of here with that crap. Needy is someone who you expect to respond basically every ten minutes. But this is 48 hours. This is 2,880 minutes. Can't spare two of those? Then fuck him.
Unless this guy just died, he simply don't give a damn about you. You need to proceed to drop him like a bad habit.