If you were to follow Dr. Ehrman on this, you'd come to the conclusion that no, the text of the NT is not reliable insomuch as we do not have the original manuscripts penned by the authors of the NT, but merely copies of copies (of copies) that contain numerous many scribal errors. Therefore (his reasoning goes), there is no possible way we can be certain what the originals truly said, and so there is no possible way we can be certain what God inspired the original writers, to write. This is of course an oversimplified summary of Dr. Ehrman's position, but it's essentially what he believes.
Contrary to this, if you were to follow Dr. White's reasoning you would be inclined to come to the logical conclusion that YES, we can view the text of the NT as reliable since there are thousands of ancient manuscripts availabe for study and regardless of the variants that Dr. Ehrman focuses on, the heart of the message contained within those manuscripts never changes - it has been the same message dating back to the very earliest manuscript nearly 1,900 years ago. Dr. Ehrman himself admits that the NT has much earlier attestation than any other book in antiquity. He is correct, even if he comes to an erroneous conclusion.
In our day where uncertainty is elevated as some sort of neo-humility, it's more important than ever to be able to give an informed, well-thought out reason for why you as a Christian believe what you believe to such questions as: Why do you believe the Bible? Where did the Bible come from? How can you be sure its reliable? Not only is this uncertainty commonplace among atheists and agnostics in our day, but its found inroads into evangelical churches as well, riding on the coat-tails of post-modern/emergent philosophy and "dialogue".
I ordered this debate on dvd recently, and just last night had the opportunity to set aside the time to watch it. It was quite literally captivating! I would strongly encourage you (you will be so blessed) to go buy this dvd today, and sit down with your family and watch it. Not only will you be informed and educated, but it just may inspire some really great discussions among you. You may want to order a copy for your church library as well.