"... influence, and ultimately change, the values of those groups that voted Democrat."
That sounds good, but it will take too long. By the time you convince enough Democratic voters that their values are wrong, the country will no longer be America and nothing can then be done to help.
If I were a Republican I would do the following:
-Immediately draft Marco Rubio and Susanna Martinez as the GOP ticket in 2016; appeal to conservatives and mainstream America on the basis that the GOP is still the party of conservative ideas; appeal to Obama voters on the basis of race, telling them they would be racist not to vote for this historic ticket.
Hey, Obama said, "Vote for me; I'm black," and his supporters voted for him twice.