Will the repentance of one who says, "I have no excuse on the Day of Resurrection" if his need is not met, be accepted, and what is the expiation for that?

Your statement, "I have no excuse before you on the Day of Resurrection," could mean two things: either it is a declaration of the reality for someone to whom the evidence has been presented, or you intend it to mean that you have no excuse for disobeying the Lord of the Worlds and for your negligence. This latter interpretation, evident from your intent, is a grave error, for you are in absolute need of God's mercy and forgiveness. No one enters Paradise by their deeds alone, but rather by God's grace and mercy encompassing them. This statement is not considered a vow, and nothing is binding upon you because of it. Seek forgiveness from God and ask for His pardon and mercy. Increase in good deeds, strive in obedience to God, and seek His forgiveness. Be keen to be among the grateful. And beware of being among those who deal with God only to fulfill a need, then turn away from Him and forget to thank Him for His blessings.