Summary: Is it possible for us to deceive ourselves into believing what is false? God says it is...
People can delude themselves into believing whatever they want.
For example, before I became a Christian (when I was 21), I was out driving my truck when I needed to turn around and go back to where I left. When I did so, I backed into a street sign and scraped up and dented my truck. Of course, I thought I would get in trouble for this, so I invented a story saying that someone hit my truck in the Wall-Mart parking lot. I had repeated this story that I knew was false so many times over the following months that it got to the point that I actually believed that it happened. Whenever I would talk about, it would become second nature, like this is really what happened. The cliche is right that says that if you repeat a lie enough times, you are going to believe it. You can deceive yourself into believing what is false.
Self-deception is a common thing that happens in some way to all of us, especially when it comes to trying to justify or rationalize something that we want to do that may be contrary to the will of God. This is even more true when it comes to those who claim that they do not believe in God. I have been spending a lot of time recently studying atheism along with ways of refuting atheists. As I have studied things that they believe, and as I have been learning things in school about what "science" teaches about the origins of the world and of life, I have seen one thing really clear: some people will put in a ton of effort to reject God, and when they do this, they are willing to believe almost anything so they can suppress the truth that God so clearly shows all of us about His existence in His creation and in His word.
God says that this will happen to those who don't want to submit to Him. This is so clearly seen in Romans 1:18-32:
"For the wrath of God is revealed from heaven against all ungodliness and unrighteousness of men who suppress the truth in unrighteousness, 19 because that which is known about God is evident within them; for God made it evident to them. 20 For since the creation of the world His invisible attributes, His eternal power and divine nature, have been clearly seen, being understood through what has been made, so that they are without excuse. 21 For even though they knew God, they did not honor Him as God or give thanks, but they became futile in their speculations, and their foolish heart was darkened. 22 Professing to be wise, they became fools, 23 and exchanged the glory of the incorruptible God for an image in the form of corruptible man and of birds and four-footed animals and crawling creatures. 24 Therefore God gave them over in the lusts of their hearts to impurity, so that their bodies would be dishonored among them. 25 For they exchanged the truth of God for a lie, and worshiped and served the creature rather than the Creator, who is blessed forever … 32 and although they know the ordinance of God, that those who practice such things are worthy of death, they not only do the same, but also give hearty approval to those who practice them" (Romans 1:18-25, 32).