If we fail to believe will God break His promise? Romans 3-4

Romans 3:3 (NASBStr)

What then? If some did not believe, their unbelief will not nullify the faithfulness of God, will it?

Paul is, in the book of Romans, explaining to the Roman, Gentile, believers the faithfulness of God.  They had slipped, or were about to slip, into the belief that since the gospel was now given to them God had rejected the Jewish nation and they, the Jewish believers, had no special place in the church.   Something, of course, the Jewish believers would dispute.  So, Paul, in this great book, is setting out to demonstrate to both groups their equal standing before is based upon God's faithfulness and grace and not their national, political, or heritage standing.   In chapter three of the book Paul is going to show them that both Jew and Greek are equal in sin - both are sinful and separate from God, unless God intervenes with His abundant grace.   In the above verse Paul wants them to realize that, yes, to the Jew were given great advantage.   Note what he said in the previous two verse of chapter three:

Romans 3:1-2 (NASBStr)

 Then what advantage has the Jew? Or what is the benefit of circumcision? Great in every respect. First of all, that they were entrusted with the oracles of God.

The Jew's were given many benefits (see Romans 9:1-5 for a better and more exhausted list).   But, they were also guilty of being unbelievers of those things God gave them.   Paul's argument is easy to understand: Does the unbelief of the creature make the Creator's promises null and void?   That answer, Paul gives in verse four of this chapter, is a resounding, NO!!  (His exact words are, "May it never be!!").   When God makes a covenant with His people, their failure to believe does not void the promise of God.  God does not give and than take back.  When God promises God means it to be so.  Paul takes several chapters to develop this theme and others important to the argument.   He somewhat returns to this very point in Romans 11:29.  Note what he says about God's promises there.   This might, perhaps, be one of the most wonderful verses to meditate upon when and after we sin:

Romans 11:29 (NASBStr)

... for the gifts and the calling of God are irrevocable.

When God promises His grace and mercy and calls us to be His children those gifts are "irrevocable."  Along with Romans 8:1, this verse might be one of the most blessed to know and hear in a sinful man's life.   God's promises are sure.   Our unbelief, fear and wayward walk does not cause them to fail.  Those things might provoke God's wrathful corrective discipline, but it can't cause us to lose the promise(s) given to us.  God is faithful, even when we are not.