Is the expression, “The Hillary Clinton Republican Primary” self-explanatory and clear-cut without reading the text?
Solution 1:
Apparently the writer is trying to say that the next Republican primary will be all about Hillary Clinton, that is, about how to beat Hillary Clinton. But the most obvious reading of the title is that it is a meeting of Republicans who are led by Hillary Clinton. Of course this makes no sense as Hillary Clinton is not a Republican and is unlikely to become a Republican anytime soon. Maybe the writer did this on purpose so that people seeing the headline would do a double-take, "Hillary Clinton Republicans? What is he talking about?", and read the article. Or maybe the headline was just poorly worded. If I was trying to convey that idea, I would be more likely to write, "The 'Beat Hillary Clinton' Republican Primary" or "The Anti-Hillary Clinton Republican Primary".
BTW I think the article is mostly the Hillary Clinton and Her Friends Fantasy Scenario. I read many pundits on both sides and this is the first time I've heard anyone say that they think Mrs Clinton is the obvious and inevitable 2016 Democrat nominee. She is one of many names being discussed. This sounds like the typical bandwagon argument: You get all your friends to say, "Of course everyone knows that ..." and hope that people believe that this is, indeed, a commonly accepted fact and so there is no need for them to think about it for themselves. But I'm getting off-topic.
Solution 2:
This year's Republican primary was all about who was going to be able to beat Barack Obama. People who supported that point of view did not support the idea that the primary was supposed to be a winnowing process to select the one candidate who best represented the Republican Party's values and policies. That this is true is evident from the way the GOP treated Mitt Romney both before and after the election. He got no respect, and the only reason he won the nomination, it seems, was that he seemed to be the sanest and least toxic candidate running for the office of POTUS -- I make that statement not to be partisan (I didn't vote for anyone because I don't live in the USA and because it doesn't matter to me who runs the country in cahoots with the big multinational corporations) but to summarize what both the media and the Republican pundits were saying about Romney and his rivals.
The phrase “The Hillary Clinton Republican Primary” doesn't suggest to me at all that Hillary Clinton leads the GOP, and the "The" in front of her name doesn't change for me the meaning of the phrase. It simply makes it clear that this is the name of the primary because many members of the GOP believe that Hillary Clinton will run for POTUS in 2016. She may, and she may win if she does, but it's far too soon to build a political strategy on this possibility alone. The author is making a serious dig at the GOP for being so narrow-minded and so swayed by yet another straw poll measuring the American public's political preferences at the moment.
Even foreign readers interested in American politics should be aware of this. I don't know anything about Halperin except for what I read in the last five minutes, but he seems not to be a terribly responsible journalist. I don't know what his political views are and don't care. But if what he says about some Republicans talking about the 2016 POTUS election is true, then his phrase seems apt.