Kasich could deliver Ohio for Trump.
Gingrich could help uniting the party and bring in the conservative base.
Corker: is he considered a good pick by the conservatives? I doubt it.
The VP choice can do little good but much harm to a Presidential nominee. Think of how badly the choice of Senator Thomas Eagleton went for George McGovern.
People pay much more attention to the Presidential nominee than to the VP nominee. Just think of the huge blunder that Mike Dukakis made when he picked Senator Lloyd Bentsen, a well-respected US Senator. The Presidential nominee was very much a Texan. Bentsen might have been enough to flip Texas if the state were close to the national average, but not as much as a Presidential nominee.
Strengthening support from the Party base? That is far from enough.
