A bit of a whimsical, "what-iffer", perhaps.

As far as church organization goes, the two type of "general authorities" (full-time leaders of the general church) are the "apostles" (of which the President of the Church is one), and the "seventies".

In general, I believe one must hold a certain office of the priesthood (or higher) in order to ordain someone to that office. The presidents of the 70 as far as I know have not been ordained apostles, so in my opinion they would not be able to ordain apostles.

However, the seventies do have a large authority in the church. Here's D&C 107:25-26 --

"The Seventy are also called to preach the gospel, and to be especial witnesses unto the Gentiles and in all the world--thus differing from other officers in the church in the duties of their calling.

"And they form a quorum, equal in authority to that of the Twelve special witnesses or Apostles just named."

That means, in my opinion, that if all the apostles were killed at once, the Presidents of the 70 *would* have authority to continue leading the church. However, (also in my opinion of course), the church would remain apostleless, barring a heavenly visitation (such as when Joseph Smith and Oliver Cowdery were ordained apostles in 1830 by the angelic ministration of Peter, James and John)