Reading through the Gospels before the semester started, God gave me Jesus' words to chew on: "Apart from Me, you can do nothing."

Really? Nothing? In a very literal sense, yes. If God doesn't allow me to take another breath, guess what? I ain't taking it. Unless He graciously continues giving me words to type and a mind to put together coherent sentences, this blog will not be written.
And yet, at the same time, it seems like He has given me a lot of freedom to take those gifts He has given and use them in a variety of different ways. Will I strive on "my own strength" to accomplish great things in hopes that people will look to me and think I'm awesome?
Here's another option: Will I trust God's leading into what are impossible situations on my own strength, depending on Him alone to come through? When I do this, I can't possibly take credit for the results. Jesus' disciples run up to Him all excited: "Even demons submit to us in Your Name." We don't see them slowly strutting up to Jesus with smug looks on their faces: “Yeah, just like we planned.”

No. The disciples were amazed! This was something supernatural that they were a part of. They spoke the name of Jesus, and the most terrifyingly evil creatures ever bowed down in submission. This was nothing Jesus' followers mustered on their own strength or wisdom. This was God using people to do something extraordinary for His glory.
"Apart from Me, you can do NOTHING!" It's amazing how quickly I forget this and try by my own efforts to do something of eternal value for the Kingdom. It's not going to happen. I can't save anybody; the Father has to be drawing hearts. I can't give just the right argument that is going to turn someone to Christ; the Holy Spirit has to be convicting of sin. I can't make anyone want to follow Jesus or love Him with all they have; God has to do a miracle and raise the dead and remove hearts of stone and replace with hearts of flesh. 
Walking with Tom Short over to campus yesterday for his first day of open air preaching, I asked him if he still got nervous before he talked. He replied, “Not nervous, but not over-confident either.” He prays each time before going out that God will show up, realizing that if He doesn't, nothing of any eternal value is going to be accomplished. Tom has been doing this for more than 30 years. I know if I were him, I would be very tempted to think, "I've heard every question, I've studied up on every response, I got this." It was so good for me to see, still, after all these years, a humble and total dependence on God's power to move. 
I was able to observe the plaza at CSU the rest of the day as God indeed did show up. It was so encouraging looking around the circle, seeing so many Rockers engaged in spiritual conversations with those listening. God answered prayers. There were soft hearts ready to listen and engage in spiritual conversations. The good news of Jesus Christ went out boldly and clearly. God opened doors for it to be received and provided for a lot of follow-up conversations. 
There's more to be done, more hearts to be drawn, more dead to be raised, more lives to be bowed down to the only One worth bowing to, and here we are, completely helpless on our own to make any of it happen. And yet we are not on our own. God makes the impossible possible: He raises the dead and moves hearts. He has invited us to be with Him as He does all this. Will we join Him in His work?
We can do nothing apart from Him, but there is nothing impossible with Him.