A failover would only fix an overloaded server by forcing people off of it. In short, that's no fix at all. You need to monitor the server and the resources used in it in order to understand the load it's under and where the pain points of that load are. Then, adjust the structures, code and server settings to deal with that load. It's possible you need to get more, bigger, better, hardware. However, without knowledge of what's happening on the system, it's impossible to know.
How much load can SQL Server sustain? Probably more than any of us can easily generate.
However, to do that, you have to set up the servers correctly. You have to design the databases well. You have to write code that's going to perform. You have to choose your indexes appropriately. You have to ensure that you're maintaining your statistics. And, finally, you have to have monitoring in place to understand where you're experiencing pain.