Israeli security forces would have swiftly engaged and killed the assassin, revealed to be a "Palestinian terrorist". Really. It would be in all the papers. Very sad, how the Palestinians would stoop to anything to stop peace, you can't trust Arafat, Abu Nidal was probably behind it, yadda-yadda, America must stand`strong behind its ally, only democracy in Middle East, peace through strength and more F-15 sales, business as usual. You'd probably get everyone from the Real Black September to the Judaean People's Front claiming responsibility for it anyway.
Begin would step down over the embarrassing failure of the IDF to safeguard this opportunity for peace, while his successor in the interim administration prior to the election would initiate a counterassassination operation against some bunch of Palestinians who would be accused of being behind it.
Sure, there will be stories about how it was really a IDF or Shin Beth bullet, but honestly there would be the same stories if it really was Abu Nidal behind the shooting.
Carter would frankly bribe the living pants off Mubarak to (out of sorrow and respect for the fallen Sadat) carry on with the peace deal, and there would probably be a very similar thing at Camp David after Mubarak has ensured the loyalty of people with influence in Egypt, or at least ensured that the only people with influence are those who are also loyal.
An interesting question would be whether Mubarak would in turn be assassinated in 1981.