This information is from past and present Gallup Polls (between 1995 and 2013) -- with each years poll containing at least 18,000 nationwide adults. The large sample gives the poll a very small margin of error -- only 1 point. The survey includes both those who claim membership in a political party and those who "lean" toward one of the political parties.
Note that among Whites there has been a small move toward the Republican Party (from 46.8% during the Clinton administration to 50.3% during the Obama administration -- a move of 3.5 points). I suspect at least half of that was due to the remaining racists departing the Democratic Party in response to their nominating an African-American as their presidential candidate (twice). Currently the Republican Party has a 9.5 point advantage over the Democratic Party among Whites.
There has been no corresponding move among Non-whites. They remain loyal to the Democratic Party, and the Republican Party has not been able to make any inroads among this group (with the slight movement being within the 1 point margin of error). Currently the Democratic Party maintains a 47.2 point advantage over the Republican Party among Non-whites.
The small movement of Whites toward the Republican Party may make some right-wing Republicans happy -- but if so, then they are denying the reality of what is happening demographically in this country. The 3.5 point move is not even enough to cover the shift in voters in the United States (where with each presidential election Whites make up about 2% less of the total voters and Non-whites increase by that same margin). That means that while the Republicans gained about 3.5 points among Whites, they lost at least double that many points among the entire voting population.
And there is very little (or no) chance of anything changing in the neat future. I doubt the Republicans can siphon off many more Whites (if any), since the remaining Whites abhor the right-wing extremism of the Republican Party. And that same extremism will keep Non-whites from considering the Republican Party as an option. Add to this the continuing demographic shift in the United States from White to Non-white, and you have a pretty grim prognosis for the Republican Party.
Unless the Republican Party moderates its views to reach out to young voters, women, and Non-whites (something the teabagger element in their base will not let them do right now), they will grow closer to irrelevance with each passing election -- and their chances of regaining the White House will grow dimmer.
