It makes sense why this is such a popular "gospel" hook these days. It gives you something to do to help save yourself (YOU made a deal with Jesus by giving Him something, so He kinda owes you), and it lets you believe your heart really isn't all that bad (He accepts your heart rather than it being co-crucified as unredeemably wicked). Pure fleshly sentiment under the curse of Galatians 1:8-9.
Some thoughts in further support on this issue...
1- The "give your heart/life to Jesus" crowd is actually Israel's Lordship salvation.
It is Scriptural. But there is a difference between merely being Scriptural and being Dispensationally Scriptural - a huge, huge diferrence as to who's meat and its' due season.
Luke 12:42 And the Lord said, Who then is that faithful and wise steward, whom his lord shall make ruler over his household, to give them their portion of meat in due season?
Israel's Stewards were to have given Israel the following, but had consistently failed to...
Matthew 22:37 Jesus said unto him, Thou shalt love the Lord thy God with all thy heart, and with all thy soul, and with all thy mind.
Notice - He was the Lord thy God - which is NOT our gospel.
Israel's "repent" was the issue of THEIR being called to turn BACK TO the God of THEIR fathers.
They had NOT been loving Him "with all thy heart, and with all thy soul, and with all thy mind."
2 - Today's "give your heart to Jesus" is about emotion; about one feeling good that one walked the aisle (a work), repented, prayed the prayer (a work), and all the rest, and as a result; one FEELS better, FEELS good about himself, FEELS close to God, and all the rest.
Its all about "FEELING" this, that, the other...
For these types, it is NOT about FAITH in an intelligent understanding of the Word.
For them, it is NOT about an intelligance based on the Word, rightly divided.
For them it is about FEELING - "I repented and FEEL better."
In contrast to Paul's point about these fool "leadings..."
1 Corinthians 12:2 Ye know that ye were Gentiles, carried away unto these dumb idols, even as ye were led.