"But God commendeth his love toward us, in that, while we were yet sinners, Christ died for us." (Romans 5: 8)
Indeed, God our Father sent His Son to die for us and as us.
We can come to God as we are, since grace is not for those who deserve it, but rather for the entire world which never deserved His goodness:
"Even when we were dead in sins, hath quickened us together with Christ, (by grace ye are saved;)" (Ephesians 2: 5)
"8For by grace are ye saved through faith; and that not of yourselves: it is the gift of God: 9Not of works, lest any man should boast. 10For we are his workmanship, created in Christ Jesus unto good works, which God hath before ordained that we should walk in them." (Ephesians 2: 8-10)
There is a teaching that has gone around, however, which suggests that we can come to Jesus as we are, and stay as we are.
Yet Salvation is so much more than our sins forgiven. We are granted a new standing, a new life, a new identity in Christ.
When we receive Jesus, believing on Him as our righteousness (1 Corinthians 1: 30; 2 Corinthians 5: 21), we become sons of the living God:
"For as many as are led by the Spirit of God, they are the sons of God. 15For ye have not received the spirit of bondage again to fear; but ye have received the Spirit of adoption, whereby we cry, Abba, Father." (Romans 8: 14-15)
The grace of God which saves us also sanctifies us:
"11For the grace of God that bringeth salvation hath appeared to all men, 12Teaching us that, denying ungodliness and worldly lusts, we should live soberly, righteously, and godly, in this present world; 13Looking for that blessed hope, and the glorious appearing of the great God and our Saviour Jesus Christ; 14Who gave himself for us, that he might redeem us from all iniquity, and purify unto himself a peculiar people, zealous of good works." (Titus 2: 11-14)
Indeed, we do come to Jesus as we are, but we become as He is!
"For if by one man's offence death reigned by one; much more they which receive abundance of grace and of the gift of righteousness shall reign in life by one, Jesus Christ." (Romans 5: 17)
"But we all, with open face beholding as in a glass the glory of the Lord, are changed into the same image from glory to glory, even as by the Spirit of the Lord." (2 Corinthians 3: 18)
"Herein is our love made perfect, that we may have boldness in the day of judgment: because as he is, so are we in this world." (1 John 4: 17)
We come to Jesus as we are, but then we become as He is.