Matthew 7:21-23 (NASB) says:
"Not everyone who says to Me, 'Lord, Lord,' will enter the kingdom of heaven, but he who does the will of My Father who is in heaven will enter. Many will say to Me on that day, 'Lord, Lord, did we not prophesy in Your name, and in Your name cast out demons, and in Your name perform many miracles?' And then I will declare to them, 'I never knew you; DEPART FROM ME, YOU WHO PRACTICE LAWLESSNESS.'"
I'm not sure I understand the question posed, as Jesus is not saying in this passage that He will reject everyone who believes in Him. He is only saying He will reject those who He did not know in an intimate way.
They will come up with many excuses, to be sure, but if He did not know them intimately, if they are not His adopted brothers and sisters, if He is not their Lord, and if they do not love Him, their excuses will fall on deaf ears.
Don't let this be you. If you do not have an intimate relationship with Jesus Christ, there is no better time than now to repent and turn to Him.
In John 6:37, Jesus states "All that the Father gives Me will come to Me, and the one who comes to Me I will certainly not cast out."