Question: Does a person have a choice when God deals with their heart?
Response: All people without exception are called to repent and believe the gospel. God holds no one back from believing. However, due to a corruption of nature all people who hear the gospel reject it. But those whom he inwardly calls by his Holy Spirit, out of all the ill-deserving sinners on earth, willingly come to Christ.
Paul declares, "we preach Christ crucified, a stumbling block to Jews and folly to Gentiles, but to those who are called, both Jews and Greeks, Christ the power of God and the wisdom of God." 1 Cor 1:23-24
As you can see from the text, the gospel call goes out indiscriminately to all, both Jews and Gentiles... but to Jews it is a stumbling block, and to Gentiles it is folly (i.e. universal rejection) - but to THOSE WHO ARE CALLED out of these groups, the power to God... they all rejected the outward call but embraced the inward call. Make sure to notice the distinction Paul makes between the two types of calling in this Text.
Likewise Jesus himself declared, "the Spirit quickens, the flesh counts for nothing ... that is why I told you that no one can come to me unless the Father who sent me grants it." John 6:63, 65
But in the same context of John 6 Jesus says "all that the Father gives me will come to me." John 6:37
Notice he says, ALL, not some, of those the Father gives him will come to faith in him.
So let's place these two statements side by side since "grant" and "give" (vs. 37 & 65) are the same Greek word here and both sentences use the phrase "come to me":