It's the truth and it's a choice.
There is nothing more you can give than your heart in it's current state. He doesn't expect you to fix it up, shine and polish it. There's no perfection required to give your heart to Jesus. And the best part, the really gorgeous part, is He'll honor the gift you've given with a greater one, His sacrifice, resurrection, and eternal life.
"But God demonstrates His own love toward us, in that while we were yet sinners, Christ died for us. Much more then, having now been justified by His blood, we shall be saved from the wrath of God through Him. For if while we were enemies we were reconciled to God through the death of His Son, much more, having been reconciled, we shall be saved by His life." ~Romans 5:8-10