By the middle of this century…whites will no longer constitute a majority of our population. In such circumstances, a nearly all-white party, which is what Republicans have become, would have no chance of obtaining an electoral majority.There are two notable problems with this argument. One, as Bouie effectively argues, as that the definition of "white" is highly malleable. In the nineteenth century, Italian, Irish, and Eastern European immigrants were shunned by Republicans as being distinct and inferior to the whites of the United States. As Bouie says, "They were seen as nearly as separate—as irreducibly different—as African Americans were." Democratic machines largely welcomed them into their ranks.
Over time, however, the descendants of those immigrants came to be treated as white and were welcomed into the Republican fold. The idea of an Irish Catholic president really was an affront to many Americans' sensibilities fifty years ago. Today, hardly anyone notices; the most recent Republican executive ticket contained a Mormon and an Irish Catholic, and it's hard to find any evidence they lost votes because of it. Similarly, there is every reason to believe that Latinos will be embraced as white as time goes on. As Bouie notes, Sen. Ted Cruz is basically considered white, and his children will be, too. And via intermarriage, the distinction between the races is becoming increasing a matter of opinion.
The other major problem with the Galston/Kamarck argument is that just as whiteness is not fixed, neither is the Republican identity. Just a few months ago, the Republican congressional leadership was widely seen as being controlled by a rump Tea Party faction, and this seemed to be hurting them in the eyes of voters. And then yesterday, John Boehner told that faction to go pound sand. Parties are, of course, highly constrained on what stances they can or can't take, but they're not obligated to follow the wishes of their most boisterous members if they think that would lead them off a cliff.
Here's a thought experiment: imagine some disease swept through the country and the only remaining voters were Jewish African American lesbians. Democrats would do extremely well in the next election, and probably the one after that, as well. Eventually, though, the more conservative politically active members of the electorate would find reasons to disagree with the others (maybe on taxation, the role of the government, social order, etc.), and they'd form themselves into a party. Maybe they wouldn't call it the Republican Party, but whatever they call it, they'd soon be competitive enough to win the occasional election.
It's worth remembering that in the 1860s, the Democratic Party was seen as the party that had led a treasonous campaign to tear apart the country and had helped instigate a war that killed roughly two percent of the population. Yet by 1876, they were within spitting distance of the White House, and in 1884 they won it outright.
All this is to say that just because the numbers currently look bad for a party doesn't mean that they're fixed in stone. Parties can react, which, in the long run, is what makes them competitive.
(h/t Jonathan Bernstein)