I used to do the same thing ... get crazy trying to do what's right, and finally realized I will never be able to fulfill the law, to live up to its expectations. I want to, but I can't (sound like Paul?) in my flesh. In my opinion and human understandings of Scripture, even "our" righteousness is as filthy rags, but the righteousness of Christ makes us perfect. What Christ did on the Cross (shedding His blood for my sins) meant that it wasn't a one-time sin He died for, but all sins I'd ever commit in my lifetime.
Yes, I still want to do what's right, and yes, I still hate it when I do wrong, but ... thank God His righteousness trumps my unrighteousness! I can never pay the debt by being perfect because I never will be. Thank God Christ paid our debt for us. Being righteous conscious (aware of what Jesus' righteousness did for us) is much more lighter on the heart than being sin conscious (continually aware of our failures). Both are facts ... our sins, His righteousness, but it's up to us what we focus on.
You're right, too, when you say there aren't many in the world who care what they do. The world is going to wax colder and colder, BUT ... where sin abounds, grace abounds more!

Our failures will never trump what Christ did in us (only in our minds sometimes), and the sin of the world will never trump God's grace (even though it may look like it). He overcame the world, and we have the Spirit of Him living in us...that same Spirit who raised Christ from the dead is in us. Isn't that awesome!
Just my two cents!