Are the words "God doesn't give you more than you can handle," in the Bible? Well the short answer is no. This comment is most likely taken from 1 Corinthians 10:13 (New International Version)
"No temptation has seized you except what is common to man. And God is faithful; He will not let you be tempted beyond what you can bear. But when you are tempted, he will also provide a way out so that you can stand up under it." This would be a great life verse to memorize so you can quote it correctly, it can help you when you are tempted, and it gives you a great opportunity to share God's Word to others in a time of need and brokenness.