Can you name one time Christie compromise with Obama? He works for a state, not the federal government. Obama will not be on the ticket in 2016. Republicans will be too worry about Hillary to care about him. If you are going to point to Hurricane Sandy, then Christie can fall back on his efforts to repair the damage and that's good ground for him. He is an executive that can fix problems. He can also highlight his accomplishments: winning in a blue state, lowering taxes, and sticking it to the teachers unions. What Republicans are not going to love that?
As for your primary people:
Bennett - Ousted at an off year Republican Convention, did not get a primary
Dewhurst -
won the original primary against Cruz who had to split with the other tea partiers, there are no run offs in presidential politics
Castle -
lost in an off year where only 57,000 voted in the primary
Lowden -
You are really going to cite this terrible candidate: barter system, bring a chicken to a doctor Nevada dodged a bullet.
Murkowski - lost a primary 2010 against a Palin backed candidate. Height of both Palin's and Tea Party's power. Still won the general that year
Crist - lost due to his support of the stimulus and Rubio being a better campaigner, Christie never voted for stimulus or Obamacare
Lugar - got hammered for his relationship with Obama (been that way since Obama was a Senator), also was his 7th reelection, they wanted a change, also was attacked for not really living in Indiana and was described as part of the Washington establishment, Christie is not from Washington though they could highlight Wall Street connections but why attack businesses?