We all know the current republican problem of fast changing demographics. Is this unprecedented? Have either the D or R parties faced a situation similar to this in their histories? If this is the wrong place to ask this question, perhaps someone could move it.
Definitely not.
Arguably this is one of the factors that doomed the Whigs (along with the weakening of the Free Soil Party, which had the votes of a lot of anti-slavery Democrats in 1848). The Famine Generation had fully settled into the urban areas of the country and the effects were very telling:
Immigrant populations, coming into the nation at unprecedented levels, strongly favored the Democratic Party (just like today). The Irish, in particular, had a very strong cultural attachment to Democratic principles going all the way back to the Jefferson era. The Federalist politicians who pushed for the passage of the Alien and Sedition Acts were pretty open about their fears of "wild Irishmen" having free rein in the country and thus passed legislation that would've severely limited their numbers and lengthen the time it took to gain citizenship.
And then a few years later the Know Nothings pushed for the implementation of some pretty authoritarian laws (that could be compared to Nazi Germany laws, seriously) that would restrict immigration/keep immigrants from voting or getting citizenship. Needless to say, that movement failed.
There is a hell of a lot of comparison you can make between Irish immigration and Mexican immigration. Both were perceived radical anti-American groups that threatened the American way of life, for starters. Seriously though, you can learn a lot from history in regards how to address the "problem" besides building fences or closing off the border. I for one don't wish to have the same oppression visited upon another group as was visited upon my ancestors. The GOP really really needs to find a way to get compassionate on the issue and silence the closed borders crowd. There isn't that much exchange that can occur when you throw up a wall.
I'm assuming the OP knows this.
A huge difference: Mexican-Americans are not as a group hostile to any part of the American way of life. They seem to have aligned themselves with one wing of the Establishment that welcomes them into political and economic life.
Enmity toward illegal aliens exists and has even proved murderous (Shawna Forde in Arizona) -- but enmity toward Mexican-Americans has never approached that toward blacks at any other time in American history or even toward the Irish of the famine-refugee era around 1850.
For a minority group in America of such size, Mexican-Americans seem placid.