No, it's never a good thing to run against your own party's incumbent president. It destroys party loyalty.
It also gives ammunition to the opposition party in the general election.
Generally speaking it's not something either party encourages.
No Republican attempted to unseat Ronald Reagan or George W. Bush when they ran for a 2nd term.
In fact the last time someone attempted to unseat a sitting president from (their own party) was Ted Kennedy during Jimmy Carter's time in office. Ted failed and Carter lost in the general election. Both parties would rather circle the wagons and present a united front when their man/woman is in office.
Hilary's next "viable opportunity" to run would be in 2016.
However if Obama is elected for a 2nd term it's unlikely that voters will stick with (the same party for 12 straight years) no matter what the state of the union is. George H.W. Bush was the last elected president of a party which held office the previous 8 years. (He followed Reagan).
Al Gore failed to win after Clinton's 2nd term and McCain failed to win after George W. Bush's 2nd term.