Is it possible to change God's mind about a situation? According to Numbers 23:19, no, it's not.
God is not a man, that he should lie; neither the son of man, that he should repent: hath he said, and shall he not do it? or hath he spoken, and shall he not make it good?
Pretty clear, right? God doesn't repent, a word which, in this passage, means "a change of mind." He doesn't lie. If He says it, He will do it.
Interestingly enough, Exodus 32 seems to tell another story. While speaking to Moses on Mount Sinai, God commanded him to go down because the people were sinning. At that time, the people had grown weary of waiting for Moses to come down from the mountain so that they could resume their journey, so they had fashioned an idol out of their jewelry and were presently worshiping that idol. God was irate, and rightly so. He had already told the people how He felt about idol worship, about having gods other than Himself. They knew better, but they sinned willingly.
God had just about had enough of these stiffnecked people, and He told Moses as much. In fact, He told His faithful servant to just leave Him alone so He could wipe the people out and start over again. But Moses spoke up for the people (though why I cannot imagine). He begged God to spare them. Moses reminded God that to destroy the people at this point would reflect poorly on the Lord Himself. And verse 14 tells us, And the Lord repented of the evil which he thought to do unto his people.
Say what? Numbers says that God does not repent, but Exodus says He does. Which is it? We know the Bible is inspired by the Spirit of God and that it contains no errors or contradictions, so how can we make sense of this seeming contrast. It's really not that difficult. The main thing to keep in mind is that words often have more than one meaning, especially words that have been translated from another language. In Numbers, we are told that God does not change His mind. In Exodus, we are told that God had a change of heart.
When Moses spoke up on behalf of the stubborn people, he exemplified great compassion, and that compassion spoke to the heart of God. Additionally, when Moses showed concern for the Lord's testimony, he proved to God that his heart was in the right place. And God was moved with compassion (just like many verses we see in the New Testament). The pleas of Moses caused God to have a change of heart. Compassion overshadowed the Lord's anger, and God relented of His decision.
The lesson for us is that prayer is powerful. Too often, we think of prayer as a formality and have the attitude that God's going to have His will and way no matter what, so why bother to pray? But, as we can see from this passage in Exodus, that's not the case at all. Our sincere, faith-filled prayers will speak to the heart of God and may even cause a change of heart. Prayer changes things, and it changes us. So, whatever you're facing today, take it to God in prayer, believing that your prayers are making a difference. It's not just a formality. It's not simply a task to be performed. We have a one-on-one audience with the King of Kings, and we can talk to Him about anything. That's not to say that we will always get what we want, but we can rest assured that God will always give what we need. Ask in faith, nothing wavering (James 1:6). Have faith in the power of prayer!