The first and most obvious argument to cosider, goes like this:
1. According to the New Testament, Jesus existed.
2. The New Testament is historically reliable.
Therefore:
3. It is very likely that Jesus existed.
The key premise is (2) which asserts the historical reliability of the NT.
Here are some Evangelical Christian defenses of premise (2) that I plan to read and critique:
Essays/Chapters
Blomberg, Craig L. "The Historical Reliability of the New Testament".
Chapter Six of Reasonable Faith by William Craig. Wheaton: Crossway, 1984.
Blomberg, Craig L. "Can the Biographies of Jesus be Trusted?" (interview of Blomberg).
Chapter 1 of The Case for Christ by Lee Strobel. Grand Rapids: Zondervan, 1998.
Blomberg, Craig L. "Do the Biographies of Jesus Stand Up to Scrutiny?" (interview of Blomberg).
Chapter 2 of The Case for Christ by Lee Strobel. Grand Rapids: Zondervan, 1998.
Craig, William L. "Rediscovering the Historical Jesus: The Evidence for Jesus". Article available on the web:
http://www.reasonablefaith.org/rediscovering-the-historical-jesus-the-evidence-for-jesus
Originally published in Faith and Mission 15 (1998): 16-26.
Habermas, Gary. "Why I Believe the New Testament is Historically Reliable".
Chapter 9 in Why I am a Christian edited by Norman Geisler and Paul Hoffman. Grand Rapids: Baker, 2001.
Metzger, Bruce M. "Were Jesus' Biographies Reliably Preserved for Us?" (interview of Metzger).
Chapter 3 of The Case for Christ by Lee Strobel. Grand Rapids: Zondervan, 1998.
McDowell, Josh. "Is the New Testament Historically Reliable?".
Chapter 3 of The New Evidence that Demands a Verdict. Nashville: Nelson, 1999.
McRay, John. "Does Archaeology Confirm or Contradict Jesus' Biographies?" (interview of McRay).
Chapter 5 of The Case for Christ by Lee Strobel. Grand Rapids: Zondervan, 1998.
Moreland, J.P. "The Historicity of the New Testament" from the BeThinking.org website:
http://www.bethinking.org/bible-jesus/advanced/the-historicity-of-the-new-testament.htm
Chapter 5 from Scaling the Secular City by J.P. Moreland. Grand Rapids: Baker, 1987.
Yamauchi, Edwin M. "Is There Credible Evidence for Jesus outside His Biographies?" (interview of Yamauchi).
Chapter 4 of The Case for Christ by Lee Strobel. Grand Rapids: Zondervan, 1998.
Books
Barnett, Paul W. Jesus and the Logic of History. Leicester and Downers Grove: IVP, 1997.
Barnett, Paul W. Is the New Testament Reliable? Downers Grove: IVP, 1986.
Bauckham, Richard. Jesus and the Eyewitnesses: The Gospels as Eyewitness Testimony. Grand Rapids and Cambridge: Eerdmans, 2006.
Blomberg, Craig L. The Historical Reliability of John’s Gospel. Leicester and Downers Grove: IVP, 2001.
Blomberg, Craig L. The Historical Reliability of the Gospels. Nottingham and Downers Grove: IVP, rev. 2007.
Bruce, F.F. The New Testament Documents: Are They Reliable? Downers Grove: IVP, 5th edition:1960, reprinted 1974.
Dickson, John. The Christ Files: How Historians Know What They Know about Jesus. Grand Rapids: Zondervan, rev. 2010.
Eddy, Paul R. and Gregory A. Boyd. The Jesus Legend: A Case for the Historical Reliability of the Synoptic Jesus Tradition. Grand Rapids: Baker, 2007.
Evans, Craig A. Fabricating Jesus: How Modern Scholars Distort the Gospels. Downers Grove: IVP, 2006.
Marshall, I. Howard. I Believe in the Historical Jesus. London: Hodder & Stoughton; Grand Rapids: Eerdmans, 1977; Vancouver: Regent, 2001.
Roberts, Mark D. Can We Trust the Gospels? Investigating the Reliability of Matthew, Mark, Luke, and John. Wheaton: Crossway, 2007.
Stanton, Graham. Gospel Truth? New Light on Jesus and the Gospels. London: Harper Collins; Valley Forge: Trinity Press International, 1995.
NOTE: I made use of Craig Blomberg's bibliography on this topic to fill out my own list of relevant books that defend the historical reliability of the NT:
http://www.denverseminary.edu/current-students/blombergs-biblical-bibliographies/#Reliability