I believe that Romans 2:4 is a strong verse for the notion that God wants even the non-elect to repent. He is genuinely or sincerely kind and patient with those who finally perish in their impenitance. When quoting this verse in conversations regarding common grace, I usually use the NRSV. I believe it best captures the thought of the goal of God's longsuffering toward sinners.
NRS Romans 2:4 Or do you despise the riches of his kindness and forbearance and patience? Do you not realize that God's kindness is meant to lead you to repentance?
Some try to get away from the idea that God's kindness "is meant to lead" (agei) to repentance, but the conative sense is recognized by several qualified exegetes and theologians. I would argue that it best comports with the sense of the passage, as the following quotes indicate:
"The very kindness (to chreston, the kindly quality) of God is trying to lead (conative present agei) thee to a right-about face, a change of mind and attitude (metanoian) instead of a complacent self-satisfaction and pride of race and privilege."
A. T. Robertson, Word Pictures in the New Testament (Broadman Press, 1931) Vol. IV, p. 335.
"The participial clause in the last part of the verse shows that God's purpose in His kindness is not to excuse sin but to stimulate repentance. The verb agei ("lead") has a conative force: God's "goodness" (chrestos) has the purpose of leading sinners to repentance (Sanday-Headlam)."
Douglas Moo, The Wycliff Exegetical Commentary: Romans 1-8 (Moody Press, 1991), page 133.
footnote #30. The present tense of the Greek is the basis of NIV leads (cf. KJV, "leadeth"). But increasingly people are understanding the verb in some sense as RSV, "is meant to lead you". This takes the present as conative, which Moule sees used "of action attempted, but not accomplished"; he understands the meaning here as "is trying or tending to lead" (IBNTG, p. 8).
Leon Morris, The Epistle to the Romans (Eerdmans, 1988), p. 113.
Wallace describes the Conative sense:
"C. Conative (Tendential, Voluntative) Present
This use of the present tense portrays the subject as desiring to do something (voluntative), attempting to do something (conative), or at the point of almost doing something (tendential)."
Daniel B. Wallace, Greek Grammar Beyond the Basics (Zondervan, 1996), p. 534.
"In his attack on self-righteous Jewish piety he shows that the goodness of God is no cheap grace which is there to be made a convenience of. It should lead to a horror of one's unwillingness to repent so that God's aim of converting men to himself may be achieved (Rom. 2:4)."
The New International Dictionary of New Testament Theology (Zondervan, 1986), Vol. 2, page 106.
"Men abuse the goodness of God, because they do not rightly apprehend that instead of indicating a purpose not to punish, it is designed to lead them to forsake their sins. The goodness of God leads us to repentance, because it shows us our duty towards a Being who is so kind, and because it gives us ground to hope for acceptance. "The word agei, "leads," says Dr. Wordsworth, Canon of Westminster, in his elegant and scholarly work on the Greek Testament, "intimates not only the will of God, but the will of man. God leads, but man may refuse to be led..."
Charles Hodge, Commentary on the Epistle to the Romans (Eerdmans, 1993), p. 48.
"The assertion that the goodness of God leads to repentance must not be weakened to mean merely that it points us to repentance. The word "lead" must be given its true force of conducting (cf. 8:14; I Cor. 12:2; I Thess. 4:14; II Tim. 3:6). The apostle is not saying that every one who is the beneficiary of God's lovingkindness is led to repentance. The presupposition of his indictment against the unbelieving Jew is quite the reverse; this Jew was the partaker of the riches of God's lovingkindness and forbearance and longsuffering and was nevertheless impenitent. Neither is the apostle dealing with that inward efficacious grace which brings forth the fruit of repentance. But he is saying that the goodness of God, including without doubt the forbearance and longsuffering, is directed to the end of constraining repentance (cf. II Pet. 3:9)."
John Murray, The Epistle to the Romans (Eerdmans, 1979), p. 59-60.
The truths in Romans 2:4, used in conjuntion with Matthew 5:44-45, constitute strong arguments in favor of common grace. They underline the important truths of God's love for all mankind (by implication), the active nature of the revealed will of God, and that he wants all to repent unto salvation. These truths do not negate the biblical facts regarding God's secret will, so they must be viewed side by side. Great errors occur when one seeks to nullify the revealed will of God by the secret will (exaggerated Calvinism), or vice versa (Arminianism).
Elsewhere, I stated that there is a conceptual connection between common grace and the universal aspect of the atonement. Here's the connection:
1) Common grace is based in intentional love (see Matt. 5:44-45).
2) Common grace is granted in order that men might be encouraged to repent (see Romans 2:4).
3) Repentance is salvation or justification (Acts 3:19, 16:31).
4) Salvation can only occur by means of a blood satisfaction available in Christ (Acts 4:12; Heb. 9:22).
5) Common grace is intentional love (point #1) granted to all men so that they might be encouraged to repent (point #2) and be saved (point #3) by means of Christ's satisfaction (point #4).
Higher Calvinists cringe when reading this because the biblical facts regarding God's revealed will have been eclipsed by an overemphasis on his secret will in their thinking. One of the purposes of my blog is to help to restore the full implications of the revealed will of God among Calvinists (even in myself as I meditate on these truths). In other words, I wish they would return to something more akin to Calvin's theology (or like the early Reformers and/or the moderates at the Synod of Dort such as Davenant). Most of them fear doing so, but God may bring a change among us. This is my prayer.