Spanish actually arrived in the United States long before the English language as Spain established colonies in the South and West before England established the Thirteen Colonies. Despite this fact, because of economic, political, and military reasons English became the dominant religion of the United States.
Spanish has challenged this dominance since the 1950s as immigrants have moved to the United States from Central and South America. There are many communities in the Southwest where Spanish has co-existed with English since the Spanish colonial times. This will most likely continue to be the case in the 21st Century.
Geography and demographics plays a major role in where Spanish is spoken in the United States. The simple answer is that Spanish is spoken most often in areas where Latin American immigrants are present. Geographically, this continues to be the Southwest in places like Texas, Arizona, New Mexico, and Southern California. South Florida is another hotbed for the Spanish language. All of these places have warm climates, which most of the new immigrants are accustomed to in their home countries. These warm weather environments also offer a demand for agricultural workers. A lot of the new immigrants from Latin America are unskilled laborers that can take advantage of this opportunity in the Southwest United States. The Southwest is also close in proximity to the homeland of a lot of the immigrants, many of whom will remain in contact with their families and possibly move back to their families in the future.
Non-skilled Spanish speakers also tend to gravitate towards urban areas in much the same way that earlier immigrants did in the 1920s. This is again done for the purpose of finding employment in low to moderate skilled labor industries.
It seems somewhat hyperbolic to say that Spanish is challenging the monopoly that English has as the language of the United States. It is not clear that Hispanic immigrants are holding on to their language and using it longer than immigrants from the past. The link below, for example, challenges this idea. If, however, we take this statement as truth, there are at least two major geographical reasons why Spanish would be able to challenge English today.
First, there is the physical proximity of the Latin American countries to the United States. This has made it so that the number of immigrants who can come from Latin America to the US today is larger than the number who could come from European countries in the past. It is easier to go overland through Mexico to the US than it was to get together the money to get from Poland or Greece to the US. Since a larger number of immigrants speaking one language now come to this country, it is easier for them to create a large bloc of people who will support Spanish-language newspapers, TV stations, and other institutions that will keep Spanish alive.
Second, there is the fact that it is easier for these immigrants to keep in contact with their home countries and cultures. This is true because, in geographic terms, the relative location of the home countries is very near to the US. This proximity is partly physical. Just as it is easier to get here from Mexico than from Italy, it is easier for a person to return to Mexico to see family and then return. This causes immigrants to keep close ties to their country of origin and could make them more likely to keep speaking the language. The proximity is also partly technological. Mexico seems closer (as do other Latin American countries) when an immigrant can get television channels from home and can text and call people back home or access websites from home. These methods of communication make it much easier for immigrants today to keep in touch with their countries and cultures of origin, making it more likely that they will keep their language.
If Spanish really is challenging English (which I strongly doubt), it is largely for these reasons.