Whether Kasich as veep candidate would deter any Republican from voting for such a ticket is unlikely (some would not support any Veep candidate who was not aligned to their thinking but it would be, I imagine a tiny minority.) The question is would the choice of Kasich make enough people support the ticket so that Trump would be advantaged?
Obviously the thinking is that Kasich could bring Ohio into the GOP's electoral college bag and no Republican has ever been elected without winning that state. The latter is true, but Ohio's electoral college vote numbers have shrunk with population shift and there are combinations of states e.g. Colorado, Nevada, Iowa which, taken together, are in fact more vital than Ohio. Trump could win Ohio and lose the election by losing those three states. Conversely he could lose Ohio and win the election with them.
This map, with the loss of Ohio shows a 269/269 electoral college tie at which point the Republican controlled house would choose the president.
Of course winning Ohio would make the Republican candidates job much easier, and there is a way, a very challenging one, where Trump's "I can win the rust states"scenario-could work. But does history show having a vice-presidential candidate from a key marginal state has made the difference for the presidential candidate? It does not.
There is not a single instance of a vice-presidential candidate whose home state 'pull" gave his presidential ticket companion the presidency except for perhaps, the "stolen election" of 1876. For all the help Lyndon Johnson may have give JFK in the south in 1960, his state of Texas was not required to give Kennedy his electoral college win. Every elected president won whether or not his running mate carried his home state. Put another way no vice-presidential candidate in a winning team gave his leader the presidency.
Indeed it is doubtful that any vice-presidential candidate had any influence on a presidential election. The only possible exceptions may be the aforementioned LBJ and, Sarah Palin who galvanized a moribund base for McCain and put him in the lead which may or may not have give him the election if the financial crash had not happened.
Looking at the map above the clearly obvious problem for the Republicans is not Ohio, rather it is Florida. As I have written many times before, if the state goes to the Dem's then it will all be over for the GOP by about 9 pm on election night-they can't recover from a loss of 29 electoral votes.
That Kasich could have any effect on Florida is doubtful in the extreme and unlike Palin he is not a base enthuser, quite the opposite.
Further Kasich is polling disastrously in his own state in the current GOP presidential candidate stakes in third place ten points behind Trump, hardly a sign of his carrying the state for Trump.
There is now a new paradigm for the GOP with the rise in importance of the Hispanic voting bloc, and there is no more important place where this support is needed than Florida. 2016 may mark the first time that the VP candidate does help the top of the ticket win by not only garnering support, like LBJ across a number of states-obviously New Mexico, Nevada, Colorado, Arizona but by making a major difference in Florida.
Marco Rubio obviously comes to mind and if he were the VP candidate then, for the first time he could possibly deliver his state, and possibly the election for the top of the ticket. However there are possible problems for Rubio in this regard. If the campaign has been a knock down drag out affair and there is bad blood between Rubio and Trump it would be hard to see how things could be patched over with a realistic semblance of "unity" that wasn't blatantly stitched up.
Rubio might also be unacceptable to the base because of his immigration stance, or they just don't trust him. With Florida so finely balanced, Obama won it by less than 1% in 2012, there is not the slightest margin for stay at home error. This is where another Hispanic possibility comes into play.
Political analysts looking far ahead to the 2016 presidential elections have advised that the GOP have a hard row to hoe given the substantial Democrat advantage in the high population states. That is of course correct and the GOP candidate would have to thread a fine needle to win in the Electoral College.
Obviously if the GOP won Virginia it would be a crucial element in forging an Electoral College victory of 270 votes, but it is not absolutely essential. The reality is that if the Republicans lose Florida then it is game over almost before it starts. Even winning Virginia and Ohio ( and the "Romney" states from 2012) still doesn't get the GOP to 270, again, either Iowa or Colorado or Nevada have to come on board for a squeaker win.
But if Virginia goes Dem, then even with Iowa and Colorado won the GOP would be 1 vote short! So, is there any hope for a Republican of any stripe in 2016 without a win, a tough challenge, in Virginia? In my opinion there would be one chance and that would be to have the current Governor of New Mexico, Susana Martinez as the Vice-presidential candidate.
Martinez is popular in her home state, is Hispanic, which might be crucial not only in New Mexico, but in Florida as well, and is seen by the base as an acceptable conservative. Being a woman might help counter the Hillary bandwagon and the ridiculous "war on women" meme if she were the Dem. nominee.
Frankly, unless there is a major swing against the Dem's in 2016, or an economic downturn, it may well be that the GOP's only chance would be to have Martinez (or Governor Brian Sandoval) on the ticket with her spending most of the campaign in New Mexico/Florida/Colorado and Nevada (a win in Nevada would allow for a loss in Iowa)-all states won by Bush in 2004 and all absolutely crucial to 2016.New Mexico was a huge win for Obama in his two elections so the odds, even for Martinez might be to high to overcome but her help in Florida/Colorado/Nevada could bring victory.