Elephant Watcher analyzed the for the last century, there has been a strong favorability towards governors as candidates. George W. Bush was a governor, Bill Clinton was a governor, Ronald Reagan was a governor, Jimmy Carter was a governor, and so on. Governors can point to their records to prove there good to be president while Vice Presidents may be stuck with an unpopular president's records and Congress is stuck with voting records.
Governor Chris Christie from New Jersey, I believe, has the potential to restore the GOP and its national popularity. He is a governor that can relate to Americans more closely than most other politicians can. He also has a personality that is well liked by many people on both sides of the aisle.
You can't save the GOP at this point. They have a nasty reputation with minorities who are growing in population, whether said reputation is warranted or not isn't important. It's there, and it isn't going away, which won't help the GOP when whites become less and less of the total population percentage.
Worse still, they keep doing things that annoy younger people, who will remember this stuff as they grow older. Things like attacking video games ( a popular hobby with youths ) standing against gay rights, supporting marijuana prohibition, and trying to keep hard working, good people from gaining citizenship ( presumably in fear of them voting for democrats if it happens ).
The elderly are dying. The newer generations are much more inclined to vote more liberal. Also the GOP's problem with the rising population of Mexican immigrants and the GOP's support for military power controlling the boarder and vigilante groups who are seen as racist against Mexicans. The GOP in my estimation has a limited time before their inevitable demise. The power of the GOP relies on the rural population where interaction with liberals is unlikely and slash and burn politics can be hard to refute when they're the only voice heard. It's more and more obvious that they only care about spending when a democrat is President. So their platform of conservative spending is seen more as a ploy that people can see through.
No, I do not believe that governors alone can save the GOP. I believe that governors can help shape and form the future of the GOP, but a fundamental shift in what the GOP believes in in order to attract different voters is the only way to save the GOP.