When you’re governor of the country’s most famous swing state and you’re sitting on a 55 percent approval rating, you’re thinking about running for president almost by definition.

“The most important (question) is can I win?” he told an audience in Detroit. “Is it a winnable situation?” Your mission, should you choose to accept it: Present a semi-plausible scenario in which Kasich wins the nomination.

The second-term governor tried to make a case that he is a different kind of leader who values unity and dislikes demonization, drawing standing ovations before a forum that members said is not prone to rising to applaud its speakers…

He told about 250 people at the Economic Club, “I’d like you to like me, but I’m not going to lay awake at night and if people here say, ‘I just don’t think he’s the guy. I’m cool with that.’ Hopefully you will — tell your friends and neighbors.”

Kasich added, “And what works in Ohio, let’s face it, folks, Ohio is a microcosm of America. It can work in our country; there isn’t any question about it.”

He portrayed himself as different. “A great leader figures out how to bring people together. We all have to stop the fighting and division. … In America today, we don’t agree on anything. … We’re all living in our silo and we’re righteous in our silos.”

Without Scott Walker in the race, he’s got a strong biographical case — executive experience, familiarity with Washington from his time in the House, and a regional pedigree that should deliver Ohio, if not Michigan and Wisconsin. With Scott Walker in the race, he’s the other guy in the field from the midwest, the one who failed to enact the type of collective-bargaining law in Ohio that Walker successfully implemented in Wisconsin. But maybe Walker will falter as a national candidate. Maybe he’ll get knocked over by scandal or seem not ready for primetime on foreign policy. That would clear some space for Kasich. But then he runs into another problem: What’s the case for him over the other swing-state governor in the race, Jeb Bush? Kasich wouldn’t have Jeb’s “Bush baggage,” but he wouldn’t have the $200 million in contributions that Jeb will end up with either. And unlike Kasich, Jeb hasn’t gone out of his way to antagonize critics on the right recently by framing support for Medicaid as some sort of religious duty for a Christian without which you’re headed for hellfire. The tea party may be only a minority faction of the GOP but it’s hard to see a guy winning a national Republican primary who’s prone to saying things like, “when you die and get to the meeting with St. Peter, he’s probably not going to ask you much about what you did about keeping government small.”

So even with Walker out of the race, it’s not clear that Kasich would have an advantage over Jeb, even on the right. And if he did get a leg up on Jeb somehow, most likely through GOPers being leery of nominating a guy named “Bush,” he’d still have Marco Rubio to contend with. Rubio’s another pol who comes from an important swing state so he balances Kasich’s big Ohio advantage. He breaks the “old rich white guy” mold for GOP nominees, he’s excellent on the stump, he commits few unforced errors, and he’s surely better known to Republicans than Kasich is. His age and lack of executive experience are knocks against him, but Rubio would generate excitement among Republicans as nominee that Kasich simply wouldn’t. Hard to see the Ohioan surviving a head to head match with the Floridian, even if he got lucky and got past Bush and Walker somehow.

All of which makes me think Kasich is really eyeing the VP slot by talking up his presidential odds. He’ll probably be a shortlister regardless, just because he checks so many boxes (especially the “Ohio” one). Tell me this, though: Which rival GOPer, as nominee, would pass on Latino stars like Rubio and Susana Martinez to tap Kasich for veep instead? The only ones who could get away with it, I think, are Jeb and Rubio since they’d already have brought diversity to the ticket (sort of, in Jeb’s case) as the party’s presidential choice. But Rubio/Kasich would be a weird match, with the number two guy nearly 20 years older than the nominee himself. Rubio’s campaign theme, contrasting his youth with Hillary’s and Jeb’s age, also makes it hard considering that Kasich is just five years younger than Clinton and actually a few months older than Bush. If Rubio’s the nominee, he’ll almost certainly pick another young pol for VP to form a youth ticket a la Clinton/Gore in 1992. Walker would be an obvious choice; Mike Lee or Tim Scott would also be possibilities. For Kasich, though, it’s probably Bush/Kasich or bust. Beyond that, it’s hard to see where there’s room for a dark horse like him either at the top or the bottom of the ticket when the field looks to have a dozen fairly solid candidates from the beginning. How do you capture the public’s imagination as an upstart when there’s a strong alternative choice no matter which niche of the party you run in?

Exit question: Kasich/Pataki or Pataki/Kasich?