A phrase that names a real danger
The words "cheap grace" do not appear in the Bible, but they describe a temptation Scripture addresses clearly. It is possible to speak warmly about forgiveness while treating sin as no big deal, or to claim Christ's name while refusing his leadership.
Paul faced this very misunderstanding in Rome. Some people might have reasoned that if God's grace shines brightly against sin, they should simply carry on sinning. Paul rejects that logic. Those joined to Christ have entered a new life, so grace cannot be used as an excuse to remain settled in what destroys us (Romans 6:1-2).
What shall we say then? Shall we continue in sin, that grace may abound? God forbid. How shall we, that are dead to sin, live any longer therein?
Grace is a gift, not a wage
Calling grace costly does not mean we can earn God's acceptance by being good enough. We can't. Paul tells the Ephesian believers that they were saved by grace through faith, not by their own works. No one gets to boast before God (Ephesians 2:8-9).
That is wonderfully freeing. You don't clean yourself up first and then hope God will welcome you. God meets sinners with mercy because of Jesus. Christ's death is the basis of forgiveness, not your effort or religious record (Romans 5:8).
For by grace are ye saved through faith; and that not of yourselves: it is the gift of God: Not of works, lest any man should boast.
The gift changes its receiver
Free grace is not powerless grace. Right after saying salvation is not by works, Paul says believers are made in Christ Jesus for a life of good works that God has prepared for them (Ephesians 2:10). Good works do not purchase salvation. They are a fruit of it.
Titus says God's grace teaches believers to say no to ungodliness and to live with self-control and devotion to God in the present world (Titus 2:11-12). Growth can be slow, and Christians still stumble. But a person who receives grace is invited into an ongoing, honest turning towards Jesus rather than a comfortable peace with sin.
For the grace of God that bringeth salvation hath appeared to all men, Teaching us that, denying ungodliness and worldly lusts, we should live soberly, righteously, and godly, in this present world;
Following Jesus is real
Jesus did not hide the reality of discipleship. He called those who wanted to follow him to deny themselves, take up their cross daily, and follow him (Luke 9:23). That is not a demand to earn his love. It is the path of trusting the King who gave himself for us.
So cheap grace says, "God forgives me, therefore my choices do not matter." Biblical grace says, "God has forgiven and welcomed me in Christ, therefore I can bring my whole life to him." If you feel your failures deeply, don't run from grace. Come to Jesus honestly, receive his mercy, and ask him to help you take the next faithful step (1 John 1:9).