God created the heavens and earth in six days, made man in his own image, and on the seventh day Genesis 2 says he rested. He blessed the seventh day, made it holy, and rested. Everything but man was spoken into existence. He is infinite, almighty God; did one week of talking a lot really wear him out?
In the first place, the text doesn’t say he collapsed from exhaustion. There is a difference between dropping dead and taking a break. Rest is a gift. Recall that when criticized for breaking the Sabbath by doing good works Jesus points out that “the Sabbath was made for man, not man for the Sabbath.” (ref) One need not be on the verge of collapse to rest, but that’s still not even the point.
God did not rest because he was tired. God leads by example. He blessed the seventh day and demonstrated the gift of rest. It is for our benefit that we rest, that we recover, that we take the time to rejuvenate before continuing with our endeavor. Adam had a vocation before the curse (he was told to tend the garden even before the first sin) but afterwords his job became work. God gave us a day of rest; the Sabbath isn’t about him needed anything from us. He does not dwell in a house made with hands, remember? (ref) God does lots of things he doesn’t have to do. He didn’t have to lead the Hebrews through the wilderness for 40 years, nor win their battles for them and give them a land flowing with milk and honey. He didn’t have to be carried around in a box (by which I mean the ark of the covenant) or hide behind a curtain inside a tent either. Jesus didn’t have to humble himself as a servant, obedient to the point of death, even death on a cross – that is also a gift from God we do not deserve and cannot earn.
Jesus washed the disciples feet. On the same night as the last supper, when he predicted his imminent betrayal, Jesus got down on the floor and washed the disciples feet. If you know what walking outside wearing sandals does to your feet you might can imagine. This was their rabbi, their teacher and master – this was the Son of God Most High – crawling around in the floor scrubbing feet. Then he asked “Do you understand what I have done?” What he had done was led by example. Jesus told his followers after 3 1/2 years to continue doing the things they had seen him do. Jesus was self-less and self sacrificing. He spent his time with fishermen and tax collectors, talked to loose women and touch lepers. He explained that he was master and Lord to the disciples, but he also was their friend and ultimately their brother.
God did not need to rest, and Jesus did not need to hang on the cross and die. We are the ones in need. We need a sacrifice that can cleanse us of our sin, we need a way back to God because we are helpless and hopeless. God does a lot of things that we need, though he is need of nothing.