Can I sin too much to the point where I have no chance of heaven?
Sin is not a matter of too much or too little. A single, unrepented mortal sin will lead to hell, whereas a life spent in mortal sin but followed by true repentance before death leads to salvation.
The problem is that many people think that they'll have plenty of time for repentance at some future point. Unfortunately, we never know if this is our last day in this world. Any number of things could befall us. There is also a grave danger that a life of sin will lead to a hardening of the heart that will make repentance an unattractive option and therefore quite unlikely.