Romans 5

For scarcely for a righteous man will one die; yet perhaps for a good man someone would even dare to die. But God demonstrates His own love toward us, in that while we were still sinners, Christ died for us. vv.7-8

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Is Jesus Christ sufficient to save even an underserving person like yourself?

Who in your life do you love and care about so much you would die for them?  Do you know anyone that would do the same for you?  Can you grasp that Christ didn't die for only the people that have it all together in their life, for only the happy people that have no struggles, for only the people that have never experience pain or hurt (there's no one in history that meets any of these), but Christ died for sinners, while we were still in our mess. 
Bible teacher Nathan Johnson explains this passage so beautifully and true for the sinner, 

Jesus Christ is God Himself. When He died for you, His death more than paid for your sins. He is the Creator Himself, as John 1:1-3 tells us. Therefore, His life is worth more than all creation…more than all of us put together. When He set out to save us by paying the penalty for our sins, He was more than sufficient to do it. His life was so much more precious than ours, that there was just no question but that it was sufficient to pay for ours. Our sin is so small and insignificant next to the price He paid to redeem us that every wrong thing we have ever done is washed away by His blood. You do not have to stare at yourself for months and years and cry and wish and despair. The Lord Jesus Christ IS the Savior of sinners like you. He DID pay for every sin you have ever committed or will commit. When He is your Savior, you WILL be forgiven and you WILL have life. Considering Him and Who and What He is, there can just be no doubt of this. (Can I Be Saved, www.precepts.wordpress.org)

The answer to my first questions is YES, yes Jesus Christ is sufficient to save the most undeserving person that includes you and every human being- we and they all just have to realize that and accept His free gift of salvation.  Do you ever struggle with thinking your sin is to grave to be forgiven?  Or do you look at someone else thinking even Jesus can't save them?  Put your trust in God's work, not man's.