I'm not sure where you're getting the idea that Latinos will soon be a majority population in the United States as a whole.
The U.S. Census
projection in 2004, by 2020 Hispanics will make up 17.8% of the total U.S. population and by 2050 that number will be up to 24.4%. While whites will fall to just half the total population by 2050 they are still twice as numerous as the next largest ethnic group.
So, currently, even if every Hispanic in the country legally (and I'm not sure if the curren population of about 35 million includes the estimated 10 million illegals or not) support illegal immigration and is willing to "strike" in support of it, then that is still only 12% of the national population in small pockets of a few states.