Sometimes to really appreciate the good news we have to first understand the bad news. It seems this is what Paul has been doing in Romans and it all comes to a head in Romans 3.
Lest the Jewish and Gentile Christians in the Roman church who have been jockeying with each other for power miss the point, Paul makes everything crystal clear:
Jews as well as Greeks are all under the power of sin. (3:9)
No one is in the right — nobody at all! No one understands, or goes looking for God; all of them alike have wandered astray, together they have all become futile; none of them behaves kindly, no, not one. (3:10-12)
For there is no distinction: all sinned, and fell short of God’s glory. (3:22-23)
Both sides need to stop their posturing for a minute and face a fact. Jew or Gentile, it doesn’t matter. Both are sinful in their own ways. Both are equally sinful. Sin, of some sort, has slithered into their hearts and is slowly taking over. At this point there is only one thing that matters and they are all the same in this way: they are doomed because of sin.
And right at the point of that depressing fact is when Paul gives the first of several statements of the gospel or “good news” in Romans:
By God’s grace they are freely declared to be in the right, to be members of the covenant, through the redemption which is found in the Messiah, Jesus. God put Jesus forth as the place of mercy, through faithfulness, by means of his blood. . . . He declares to be in the right everyone who trusts in the faithfulness of Jesus. (3:24-26)
It isn’t how good we are that matters, it is how good Jesus was. It isn’t what kind of blood we have running through our veins that matters, it is whether we have been covered by Jesus’ blood. It isn’t the rituals we have done that save us, it is the ritual of sacrifice that Jesus did that saves us. Jew, Gentile, Greek, Barbarian, American, Afghani, Iranian, devoted church attender, or tortured soul — it doesn’t matter. We are all the same at the foot of the cross. Sinners saved by grace.
A Kingdom Year 
After reading the Quran last year, I now see this chapter as the major difference between Christianity and Islam in my eyes. I am again impressed (amazed, joyful, thankful) that God gives me His righteousness out of His love for me. No matter how many good things I do, I cannot be “good enough” to be righteous on my own. I do have faith in the Creator God, Jesus the Messiah, my Holy Spirit. I hope and trust that my life is, and will be, lived in response to this free gift.
I am having the same experience this year after reading the Qur’an last year. My Muslim friends still tell me I don’t understand their religion correctly (or that I don’t represent mine correctly) but this chapter and the two that follow are so starkly different from any other worldview available in the world.
“So, what if, in the course of doing that, some of those Jews abandoned their post? God didn’t abandon them. Do you think their faithlessness cancels out his faithfulness? Not on your life! Depend on it: God keeps his word even when the whole world is lying through its teeth.”
This is a wonderfully incredible thought. God is faithful even when we are not. How could it be grace otherwise?
But it sets me to wondering. Is there a limit to his faithfulness? Is there anything a person can do to make God say that is too much? Is there a limit to God’s grace?
This same passage took out to me as well.
As for your question . . . I would say the only limit to his grace is time. As long as there is time, there is grace.