Joe Ravi [CC BY-SA 3.0 (http://creativecommons.org/licenses/by-sa/3.0)], via Wikimedia Commons
The reason that the Speaker of the House would take over today is because of the Succession Act of 1947. In 1947, when Democrats controlled both the House and the Senate, the Succession Act was passed that made it so the Speaker of the House would become President in the event that the President and Vice President were removed from office.
What made this act interesting was that it replaced an older act, the Succession Act of 1886. This act in 1886 made it official that the cabinet officials were to take over in the event of the President and Vice President's removal from office. This was passed shortly after the assassination of Abraham Lincoln and the rapid impeachment fo Andrew Johnson. At the time of Johnson’s impeachment it was made apparent a constitutional crisis would arrive if he was removed, many cite this as the reason the Senate didn't get the vote to remove him passed.
To make things more interesting the Succession Act of 1886 was actually a reversal of the Presidential Succession Act of 1792. That's right, the Succession Act of 1947 was actually a reversion to the 1792 act.
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Source: TTN staff