Republicans made marginal gains among non-white voters in 2014, but even those (generally) small improvements would have elected Mitt Romney president if that electorate had been present on election day 2012, according to a new analysis by the Republican polling firm American Viewpoint.

"Even if you keep the more diverse 2012 electorate (just 72 percent white), but give Romney the share of the vote that Republicans got with minority voters in 2014, Romney would have turned a four-point loss nationally into a three-point win," conclude Linda DiVall, Randall Gutermuth and David Kanevsky in a memo sent to me Monday. By the calculations made by the trio, Romney would have won 50.5 percent while President Obama would have taken 47.6 percent. (The memo doesn't get into electoral college breakdowns.)

Here's the math.

In 2012, Romney won 59 percent of the white vote, which comprised 72 percent of the overall electorate. In 2014, Republicans won 60 percent of the white vote, which was a slightly larger 75 percent of the electorate. The real changes in the electorate — and why Republicans won in 2014 and lost in 2012 — were among non-white voters. Check out the chart from American Viewpoint:

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Not included in the chart but worth noting: The percentages of the electorate that each of these groups comprised in each of these elections. Here's that:

* Blacks: 13 percent in 2012, 12 percent in 2014

* Hispanics: 10 percent in 2012, 8 percent in 2014

* Asians: 3 percent in 2012, 3 percent in 2014

At one level, this is not a terribly surprising conclusion. The 2014 election was a lot better one for Republicans than  2012 — as midterms tend to be. What is fascinating is that, at least according to the American Viewpoint memo, the reason the electorate was better for Republicans was not only because it was whiter, which it was, but because Republicans found ways to do better among non-white voters.

The key question here is whether the successes Obama had in 2008 and 2012 with minority voters are tied uniquely to Obama or more broadly to the Democratic Party.  While Democratic presidential candidates were winning black and Latino voters comfortably pre-Obama, the data cited by American Viewpoint suggest that even incremental gains among non-white voters by Republicans can make the difference between winning and losing.

Of course, the flip-side argument can also be made. Romney won white voters by the largest margin since Ronald Reagan in 1984 — a fact that many Democrats attribute to Obama's race. Assuming that Democrats nominate Hillary Rodham Clinton in 2016, the argument goes, the massive margins that John McCain (in 2008) and Romney (in 2012) enjoyed among white voters will be lessened — making the number of non-white votes that the Republican nominee would need much higher.

The broader point of the American Viewpoint memo is twofold: (1) the GOP must compete for the non-white vote to be competitive nationally in 2016 and (2) the 2014 election shows that if Republicans attempt to compete for the non-white vote, they can make (some) inroads.

On the first point, they're absolutely right. My favorite chart from the 2012 election is this one, which breaks down the white/non-white votes received by Obama and Romney.

The above chart is made all the more alarming for Republicans when combined with this one that shows the declining percentage of the white vote as a factor of the overall electorate.

The question for Republicans is whether they can repeat their 2014 gains among non-white voters — or come close to them — in 2016. If so, winning the White House may be out of their reach.