Just to throw a wrench in the clockwork, what if all predecessor's cabinet members were either born in foreign countries, or had not yet reached their 35 birthdays or hadn't lived in the country for at least 14 years, or something like that, so that none was constitutionally eligible?
That's a fun question too. At what point does the line of succession go down to you? Or me?
According to the the government's Common Documents site, "If a statutory successor is serving as acting President, Congress may, but is not required to, call a new presidential election."
My bet is that Condi would last about a millisecond as president with this congress.
That could be a great movie - the lone postal worker is left as the highest-ranked federal employee after the [whatever] attack and is thus forced to lean the recovering United States of America out of the ashes.