A lot of us are of the opinion that a failed first rush pretty much dooms your macro. While this is true, it doesn't mean you can't all-in and counter your opponent's attempt to "get more ahead" by expanding. The following pro game shows how a failed 6pool rush by July leaves him very far behind in economy. However, instead of his Protoss opponent going for a 4-gate counter, HongUn decides to "get more ahead" (as emphasized as the "right" thing to do by Day9 and Artosis), and expand off 3 gates.
JulyZerg vs. HongUnPrime
July foils this attempt with a large Zergling push, which, despite forcefields, allows him to eliminate his opponent's army and push him back into his main. July Zerg expanded just prior to the push, leaving him on 2 bases to his opponent's 1 base, and able to make drones without fear of counter.
I'll leave you to watch the game (which anyone should be able to watch, even without subscription), to see how it ends.