I remember when Philip Augustine made his debut here, he mentioned he was doing academic work on the historical background of Israel’s sojourn in and Exodus from Egypt. Recently, I have been re-reading articles on the matter in “The Oxford History of the Biblical World” (ed. M. Coogan), as well as various online articles.
To be sure, the dating question is not easy. If we take the reference to Pithom and Rameses (Exod. 1:11) at face value, then this acts as a terminus post quem: the Exodus cannot happen before the reign of Ramesses II (assuming these projects were begun under Seti I). However, there are some possible references to Israel in the land of Canaan before this point: e.g. the “Shasu of Yahweh” mentioned in a topographical list at the Temple of Soleb, built by Amenhotep III c. 1400 BC (http://www.biblearchaeology.org/post/2010/03/08/The-Name-Yahweh-in-Egyptian-Hieroglyphic-Texts.aspx).
Furthermore, the destruction of Jericho as described in Joshua has traditionally been viewed as problematic by scholars. Kathleen Kenyon excavated Tell es-Sultan, a site identified with Jericho, and concluded that it was destroyed c. 1500 BC by the Egyptians, not the Israelites. It was unoccupied after this point until much later. There was a small unwalled settlement nearby, however. This interpretation of the archaeological data presents a problem for the Biblical conservative: either there was no conquest of Jericho, or there was a conquest, but the story that “the walls came tumbling down” is a fiction.
In response to these sorts of problems, David Rohl proposed a “New Chronology”, but this has largely been rejected by other scholars in the field (though they have made some minor revisions as a consequence of his research). Conservative scholars continue to work with the traditional chronology and progress has been made to support the historicity of the accounts in Genesis, Exodus, and Joshua, but there remains a divide between the camp of an early date for the Exodus and the camp supporting a late date. For interesting articles on the subject, see: http://www.biblearchaeology.org/ .
For me, the Exodus is not a negotiable event. I am comfortable with various strands of interpretation within evangelicalism, but denying the Exodus is not something I can support. Exodus has many lessons to teach us, but two of the central ones are that God acts in history and that God is faithful to His people. Once we deny something like this, we start down a slippery slope that divests our faith of its supernatural and historical elements. Once these are stripped away, we have little reason to believe that God will intervene again in the future. If we lose belief in the Atonement and Resurrection, we become, to use the Apostle Paul’s words, “the most miserable of all men” (1 Cor. 15:19).
To be sure, Jesus is the foundation of our faith (Heb. 12:2). Apart from Him, we can do nothing (Jn. 15:5), while through Him, we can do all things (Phil. 4:13). Nevertheless, Christ came through Israel – when we attack the history of Israel, we attack the salvation story of which Jesus is the centre.