Here is the relevant portion of the transcript I referenced. Again, the video is here.
Lauer: “Famously during the campaign you said you could not support him (Trump)…Have you changed your mind based on anything you’ve seen during the transition?”
Governor Schwarzenegger: “Well, what changed was that now he is elected. And now it is very important that we all support the president, and that we all come together and we stop whining and it becomes one nation.
“As Obama said many years ago it’s not blue states and red states — it’s the United States of America. And there’s a great letter that I just dug up the other day that President Bush, the first, wrote to President-elect Clinton. And he said ‘I’m in my office right now and I just want you to know that I respect this office and I respect that you won and you are my president. And I want you to be very successful because if you are successful then the country is successful.’
“And this is exactly what I feel about Trump. It’s what I felt about Obama or anybody. When someone is elected then you go 100% behind them and you help them and help them shape the future of the country.”
Lauer: “That’s not — unfortunately — not how Washington works.”
Governor Schwarzenegger: “No, no. I mean, it’s not. But that’s the ideal. It doesn’t always work like that. And it’s very hard for people to do that. But that’s the effort we all have to make.
“I’m 100 percent behind him and I want to do everything that I can to help but as you also know I’m an environmentalist so to me it’s very important that at the same time — and it’s one of the reasons why I couldn’t go with Trump — I want to make sure we’re going into a clean environment and a clean future because that’s what we did in California and we proved in California by rolling back our greenhouse gases 25% and by going green, we still have a better GDP growth than the whole United States has.”
Lauer: “You still speak like a politician, and during the campaign, you said were you eligible, you might have run. Do you think you could have won, at least in the primaries?”
Governor Schwarzenegger: “That, you never know. You saw what happened this last year. Everything that people predicted didn’t happen and it turns everything upside down. I ran in California and I won easily because I was an outsider at that time and they looked for an outsider. And the same happened with Trump. They looked for an outsider.
“People are very upset at what is going on in this country, that both of the parties cannot come together. And they hope and pray that this guy — this Trump — can both bring both of the parties together, and hopefully does not run it as a Republican administration, but run it as Democrats and Republicans coming together because that’s the only way you can create true action.”
Lauer: “Do you think he’s a true Republican?”
Governor Schwarzenegger: “It doesn’t matter. You have to be, in the end, a public servant, not a party servant. I hope he is not a straight Republican. I hope that he is a public servant, that he sees himself serving Democrats and Republicans. That’s the important thing.
Lauer: “You know what it’s like to make the transition from business and entertainment to politics, so offer him a piece of advice. You talked about advice in the other direction. What’s the most important thing he needs to know about the world of politics that he might not know?”
Governor Schwarzenegger: “I think the most important thing, as I said, is to keep working with the other party, to bring Democrats and Republicans and independents and decline-to-states — all of the people — together because in the end, you do not want to just take from the pool of Republicans because you only get 50% of the brain power of the United States. If you take people from both parties then you get 100 percent of the brain power.”
“And let me tell you something — there’s so much brain power in the United States. This is by far the smartest country in the world and the best country in the world and now the trick of it is to go and make it even better.”