That is different from coat-tails crossing state lines. Show me the evidence that a presidential candidate's performance in Ohio has any bearing on congressional races in New York. The congressional races in New York could be impacted by the presidential race in New York, but not Ohio.
No, it's not. That popular presidential candidates gain seats for the party nationwide (and unpopular presidential candidates lose seats for the party nationwide) indicates that a candidate's overall performance affects congressional (and mayoral & gubernatorial) races across the whole country.
As Ohio is a key battleground state that gets the attention of all voters, then the presidential race in Ohio can reasonably affect the congressional, mayoral, and / or gubernatorial races in NY, NH, KY, MO, MI, MA, etc.
The main point stands -- Kasich's refusal to help Trump is harmful to the Republicans across the whole nation.
John Kasich may be looking at 2018 and 2020. He is savvy enough to recognize that Demagogue Don may do more harm to the GOP by winning than by losing. Donald Trump shows all the signs of the sort of President who gets defeated in his reelection bid: a despotic style of management, a tendency to vilify opposition as scapegoats, an inability to fit the ways of a political culture of which he is not a part.
He would be Jimmy Carter without the brilliance, integrity, caution, fundamental decency, freedom from corruption, and such political acumen as Carter had. Basically I have stripped Jimmy Carter of his non-ideological merit. That makes a thoroughly dreadful President. So the Democrats run someone his ideological antithesis who is also a smooth talker... think of a liberal version of Ronald Reagan. Heck, maybe America could repeal the 22nd Amendment for what will then seem the best President since FDR.