There is no such thing as a secession petition to the white house.
You have petitions in the states, delivering signatures to the State Secretary of State (at least in Texas)
But I believe the WhiteHouse.gov website (under 0bama) established the petition tool as a vehicle for anyone to use regarding any matter.
Correct. It's meaningless -- secession is achieved by an action of the People themselves, acting as their States (NOT the "state government", because [state gov't.] does not equal [State] does = People), to dissolve their compact with the other States.
During the 1832-3 Nullification Crisis, when secession came to the fore as a possible remedy for the constant attempts by the industrial Northeast to impose strong tariffs on the import trade to support the Millocracy, Daniel Webster and other political theorists changed their language about the Constitution and their theory of the Union, to make the Union into a deadfall trap, which once entered into became an unbreakable beartrap of permanent and eternal Union even against the wishes of the People.
Webster et al. were simply catering for the desire of the Millocracy and manufacturers for a permanent, captive customer base whom they could charge high prices without recourse for the buyers.
Lincoln enforced their "New Deal", "living" Constitution by armed violence.