Thinking about this in terms of politics, I think Kasich has almost backed himself into a corner with 3C. There's very little downside to him turning down the federal money. It's almost assured that the people who voted for him don't care for rail (certain urban conservatives excepted, of course), and he's been saying for months now that he'll cancel the 3C line if he's elected. If his core constituency doesn't care about rail and if he's been campaigning on it for so long, there's very little downside to turning down the federal money.
I think Kasich's only "out" is the freight railroads. Unfortunately, he's staked himself against finishing the environmental studies. If he allows those to finish, however, he could reasonably argue that the federal expenditure would, in fact, improve freight movement (as he mentioned in his letter to President Obama). From where I stand, I think the best bet to get a change of heart from Kasich isn't arguing the merits of 3C passenger service, but arguing the merits of freight rail as a result of 3C passenger rail. Of course, rejecting 3C money is a win-win for Kasich in the eyes of his base no matter how the money is spent, so I think the freight railroad "out" is a narrow opening indeed. In any case, I'll be writing to Kasich as a generally conservative young professional to let him know that part of my disinterest in staying in Ohio after receiving my masters is a result of his lack of vision for passenger rail.