- Jesus died by crucifixion
- His tomb was found empty
- The disciples believed and preached He is risen (indeed)
- Paul the church persecutor was converted
- James the skeptic was converted
As I described before, and has been laid out elsewhere, the hypothesis that makes the most sense of all five of these "facts," by far, is the resurrection as described in the gospels. (For a good treatment of this, see here.) However, most skeptics do not accept this conclusion.
But what kinds of counterarguments are presented to avoid this conclusion? Are they well-thought-out rebuttals to the conclusion? Plausible alternative explanations? Yes, attempts have definitely been made at alternative explanations, although none have been shown to be plausible. In fact, they mostly hold the day for skeptics simply because they are naturalistic explanations and do not have to "invoke" a divine intervention. So while they have poor explanatory power and scope, they are still preferred (by those who wish not to believe) because they leave out God. (This is of course not an argument, but the result of a presupposition; of a philosophical precommitment to naturalism, but I digress...).
However, in talking to atheists, I have found the most common reason given to avoid the resurrection conclusion is they are skeptical of Habermas's claim that these "facts" are agreed upon by the majority of scholars. In other words, the Minimal Facts Approach has mostly come under fire not because the historical "facts" are not agreed upon by scholars, but instead because many non-believers want the statements that "the vast majority of scholars agree on this or that fact" to be peer reviewed. Folks do not trust Habermas when he says these "facts" are agreed upon. In other words, the most intense objections are not well thought out rebuttals to the data or to the inference drawn from the data, but instead attacks on the integrity of the Habermas and Licona. That is when you know you have a good argument.