We shall see . . .
Prior to President Bush, two US presidents, John Quincy Adams, and Benjamin Harrison, were the progeny of previous Presidents (obviously JQA's father was President John Adams; Harrison's grandfather was President William Henry Harrison).
JQ Adams did not win the popular vote or the electoral vote, and was instead appointed by the House of Representatives.
Like President Bush, Harrison lost the popular vote, but won the electoral vote and was placed in office. Prior to President Bush, he was the last President to lose the popular vote and win the election.
Both men served one term and were voted out of office by landslides, in favor of the candidate they had beaten in the previous election (in Adams' case, Andrew Jackson; in Harrison's, Grover Cleveland).
I imagine the election would be quite a bit closer than those in which Jackson and Cleveland won, though, regardless of the outcome.