Let us consider the merger of the United States and Mexico! Welcome MexicUSA!
I sometimes hear we need to limit immigration or else Spanish will someday overtake English in the United States. Is that possible? What would a hypothetical US-Mexican country be like demographically?
First, let me say this is a wildly hypothetical example. Mexico is a proud country and a merger with the United States is as unthinkable to most Mexicans as it is to most Americans as well.
I bring up a US-Mexican merger simply to show what it would be like demographically, as an extreme case, since it helps address whether there are linguistic or cultural challenges to the United States from a half million or million immigrants. Let us not talk small ball but instead consider welcoming all of Mexico as immigrants all at once!
Mexico has 112.4 million residents.  The USA has 312.9 million residents.  In our new MexicUSA, the old Mexico will account for just 26% of the new US population.
But what of the future? Isn’t Mexico growing faster? Even in 2050, the old Mexico population is projected to be 132.3 million , compared to 402 million in the old USA , meaning old Mexico would actually drop a fraction to be just 25% of MexicUSA.
That certainly does not suggest Mexico would dominate the MexicUSA.
Most Mexican elites learn English. Many study in the United States. The last three Mexican presidents (Felipe Calderon, Vincente Fox and Ernesto Zedillo) all had degrees from top US universities. I have been unable to find an exact statistic on what proportion of Mexicans, whether elite or general population, speak English, I did find this quote: “As far as second languages go, a relatively large number of educated Mexicans (and those with little or no education who have immigrated to the US and returned) have different degrees of fluency in English.”  Also, “on an every-day basis most Mexicans listen to contemporary music such as pop, rock, etc. in both English and Spanish.” 
Evidence of the popularity of American English culture can be found on the Mexican music charts. In 2012, through May, the #1 spots are dominated by English language albums from non-Mexican artists (Adele, Madonna, & One Direction). Contrast that with the almost exclusively English language pop charts in the United States. The Mexican chart’s top Spanish language album is from Yuridia, who lived in Arizona for nine years and speaks English. 
It is well-known that Mexican elites in business, politics and culture generally speak English. This is, of course, common for elites worldwide. In MexicUSA, the political, business and cultural leaders from the former Mexico will be able to conduct themselves in English.
An interesting piece of immigration assimilation is intermarriage. It has long been extremely high amongst Asians and Hispanics. “Among all newlyweds in 2008, 9% of whites, 16% of blacks, 26% of Hispanics and 31% of Asians married someone whose race or ethnicity was different from their own.”  Twenty-six percent, of course, means one out of four. I know many Hispanics who are married to Anglos. Their children are as “American” as anyone else and always speak English.
Some argue Hispanic immigrants in the USA, whether from Mexico or elsewhere, do not speak English. That is simply untrue over time. Hispanic immigrants learn English and their children speak it better. By the third generation, many solely speak English.
Twice I had Latina girlfriends, both of whom spoke English. One was an immigrant from Mexico and the other, born here, had virtually no accent and hardly knew more Spanish than me! I have had many Hispanic friends and co-workers and invariably they speak English, usually fluently.
“Among second-generation Hispanics, 92 percent speak English well or very well, even though 85 percent speak at least some Spanish at home. Eleven percent of Mexican second-generation children speak only English at home, compared to five percent in the first generation.” 
“English-only is the predominant pattern by the third generation. These children speak only English at home, making it highly unlikely they will be bilingual as adults… The level of English monolingualism is lower among Hispanics, but, at 72 percent, it is still a clear majority. 71 percent of third-generation Mexicans speak only English.” 
The evidence is clear. Even in the extraordinarily unlikely instance the United States absorbed its Mexican neighbor to the South, the “old” USA would still comprise 75% of the combined population. Mexican elites already speak English and often attend US universities. Many Mexicans listen to American pop music and otherwise follow American culture. Mexican-Americans in the USA learn English over time with second generation children speaking English. By the third generation, almost 3/4 of Mexican-Americans speak only English. Intermarriage rates remain quite high so that millions of 2050 Americans will be of mixed Hispanic-other ancestry.
A half million or million more – or even ten million more – immigrants will never swamp English as a language, no more than your own ancestors’ Yiddish, Polish, Greek, Dutch, Tagalog, German, Italian, Cantonese, Lithuanian, Ukranian, Czech or Swedish held you back from learning English. Do you even speak your ancestors’ native tongues? Probably not.
 http://en.wikipedia.org/wiki/mexico retrieved 1/27/12. Technically, Mexico is called the United States of Mexico.
 http://en.wikipedia.org/wiki/List_of_number-one_albums_of_2012_(Mexico)#cite_note-5 retrieved 5/17/12.
 http://en.wikipedia.org/wiki/United_states retrieved 1/27/12.
 http://en.wikipedia.org/wiki/Languages_of_Mexico retrieved 1/27/12.
 http://www.migrationinformation.org/Feature/display.cfm?id=282 Emphasis in the original.
Pictures (flags, Yuridia, Mexico maps) from Wikipedia Commons.