What if OBOR was proposed to be a joint US-China endeavor?

[Qaa]

I watched a recent talk John Thornton (currently at Tsinghua University, formerly director of Goldman Sachs) gave at the University of Texas (link here, the anecdote is from approx 21:00-23:00). He tells an interesting story at one point:

- so John Kerry told me that, I think it was 2013, he was the senior American at one of these international meetings that Obama could not attend for one reason or another and so he was the person who took the meeting with Xi Jinping and Xi Jinping in that meeting said to John Kerry, "By the way, let me tell you about something I'm thinking about."
And he laid out the One Belt One Road [program]. And Kerry said to him, "Oh that's very interesting, why don't we do this together?" and Xi Jinping says "That's a great idea, let's do this together."
And Kerry came back to Washington and he said, "Before I got off the plane the Treasury mandarin said 'cut his legs off' and there was no chance it was ever going to happen so it never got to Obama's desk."

It must have been shut down because of either fears of how it would play electorally, concerns about the viability of getting it through Congress, geopolitical concerns (maybe how it would play in allied Asian/Oceanian countries?) or some genuine Treasury issue that prompted the veto. I don't know jack about what the US Treasury and the Fed do so let's omit the latter from discussion.
Suppose the parts of Washington that are managing the Kerry trip in April 2013 are a little bit slow on the ball and the topic gets to Obama. He holds a little cabinet discussion and they decide to put some feelers out to the House and Senate to gauge the viability of it, but this leaks and the whole idea becomes front page news.
How does this change Obama's second term? How does this change the 2013 Australian elections? I presume in the latter case Rudd is still massively ousted.