Those briefed on Kasich’s plans say he’s begun a concerted push to lock down the support of Murdoch, the Australian-born media tycoon who is an influential voice in conservative circles, and was hopeful he could be brought aboard. The two have long been close: Murdoch was Kasich’s boss during his six-year tenure as Fox News host, and during Kasich’s 2010 gubernatorial bid he convinced Murdoch to make a $1 million contribution to the Republican Governors Association. When they are both in New York City, Kasich and Murdoch make plans to see one another.

But Murdoch, those familiar with the effort say, hasn’t yet committed to Kasich, and has said that he has many friends in the contest. He has previously pointed to Bush, Scott Walker, and Chris Christie as candidates he particularly admires.

There’s little question that Bush is a serious obstacle to Kasich. Both see themselves as serious, cerebral men with unrivaled policy chops. And both are seeking to win over the party’s pro-business establishment. Leaving nothing to chance, in recent months, the former Florida governor has launched a mission to secure support in Ohio, robbing Kasich of prospective fundraising dollars in his home state before he gets his campaign off the ground.