I would like to contribute some thoughts on this, in defense of Fr. Stravinskas.
Now, I have watched the entire debate and, I admit, Fr. Peter Stravinskas did not do well. James White is renowned for his skill as a live debater. I think the good father was just a little flustered and overwhelmed, and he wasn't able to anticipate all of the arguments that White would raise. If Fr. Stravinskas lost, it wasn't because of any weakness in the Catholic position but because of weakness in the man presenting it.
His response to the questioner in the crowd was particularly unfortunate. He articulated the Catholic position in a very sloppy and inadequate way. But, I know what he meant to say and so I would like to articulate that with more precision. I'm sure some of you will think that I am "eisegeting" the priest's words or saying that he meant something that he didn't actually mean, but I'm telling you, I know what the Catholic position is, I know what he believes, I know what the Church teaches about this. Whether you accept that or not is up to you.
Now, Catholics believe that when you sin, this has an eternal effect (on your relationship with God) and a temporal effect (on the Body and really the world). Suffering, death, pain, sadness, all of these are the conseqence of sin. They are "temporal" consequences b/c they effect our experience of this world and of each other, which is a temporal existence, or an existence confined by time.
We also believe that every Christian has a responsibility to rectify or remedy the negative effect that there sin has caused. They rectify the eternal effect through conversion of heart and repentence. They rectify the temporal effect by responding to the grace of God which compels us to perform acts of charity and to obey the command of Christ to love one another. Just as sin wounds the body, charity heals the body, uplifts the body, edifies the body. Almsgiving is one of these works of charity ("love") that builds up the body and rectifies the negative consequences of sin on the body.
If you do not properly rectify the temporal consequences of your sin in this life, then this remains as an imperfection on your soul when you die. Since these are temporal consequences of sin, they have no effect on your eternal destiny. So, a person can die and be fit for heaven while still having these imperfections on his soul (attachment to sin, or "concupiscence" and venial sin are other such imperfections). Since nothin unclean shall enter heaven, God, with the grace that he won for us on the Cross, cleanses us of these imperfections. God is a refining fire, and so the soul that must undergo this purging by God will undoubtedly experience some suffering. But, he also has the knowledge that heaven will be his, and this undoubtedly sustains him.
Knowing all this, one is able to finally understand what Fr. Stravinskas meant when he said, "Pay it now or pay it later." In other words, you can pay for the temporal consequence of your sin now by doing acts of charity (motivated by God's grace) or you can pay for it later, by undergoing the the purging of God. It's not like you can write the Church a check and forgo this purging. No one is paying there way out of Purgatory. Almsgiving is simply one of many good works that build up the body and rectify the temporal consequence of sin.
I hope that helps.