Grace and more grace

Grace:
Upon preparing for my Bible study on the Grace of God for tomorrow evening, I came across this verse (in red): Titus 2:11,13,14 " For the grace of God has appeared, bringing salvation to all, training us to renounce impiety and worldly passions, and in the present age to live lives that are self-controlled, upright, and godly, while we wait for the blessed hope and the manifestation of the glory of our great God and Savior, Jesus Christ."

So the question that follows a little later in the study about this verse is:
Although God offers salvation to every person, why do only some receive it?

Does God really offer salvation to every person? If God's grace is irresistable, how can anyone refuse it?

I have been looking for an answer in the book "Know your Christian Life" by Sinclair B. Ferguson, and came across the concepts of "General Calling" and "Effectual Calling" which addresses the issue, but I can't help thinking the explanation a little to convenient. Being that there aren't any Calvinists in my Bible study, I thought I would try to represent... so I better read up on this some more.



more grace:
Blockbuster now has a seven day grace period for returns. This is excellent news for me, and upon being told this by the cashier, I replied, "That's great, I need more grace." The cashier let out a stifled laugh. I don't think she knew what I was talking about.