The amendment to the Senate's immigration reform bill to which the article refers would not make English the "official" language of the US. It would declare English to be the "common and unifying" language of the country.
The exact language as it currently stands is:
The Government of the United States shall preserve and enhance the role of English as the common and unifying language of America. Nothing herein shall diminish or expand any existing rights under the law of the United States relative to services or materials provided by the government of the United States in any language other than English.