I have traveled by this sign on several occasions, and it always puts something in my crawl when I read it. "Do your best and Jesus will take care of the rest". It's really hard to give the benefit of the doubt on this one. However, I am not sure of the context in which the phrase it meant to be taken. I am wondering, what is "the rest"? How does this phrase line up with our declaration that "Jesus paid it all"? Also, my mind thinks toward Philippians 3:1-7, and Paul's litany of "his best". When he finishes listing his "best", he doesn't then cry out to Jesus to take care of the rest. Rather, he calls "his best" all "dung" (think cow manure) when compared to the righteousness he received from Christ's perfect and sinless life through faith. His "best" wasn't good enough and never would be. So, when it comes to righteousness before God, our best is never good enough and never adds anything to the imputed righteousness we receive from Christ through faith.
A better sign post might be the words from a recent hymn:
In Christ alone my hope is found, he is my light, my strength, my song
This cornerstone, this solid ground, firm through the fiercest drought and storm
Thank Jesus today, he gave his best and it was better than good enough!