Illegal immigrants don't steal across the Mexican border because they lack the patience to wait their turn in line. They do it because there is no line for them to wait in. The great majority of immigrants who enter the United States lawfully qualify for visas because of family ties: They are lucky enough to be related to a US citizen.
For them, there is indeed a line -- the waiting time for a family-based visa can take upward of 10 years. A smaller number of legal immigrants are granted visas because they have advanced degrees or specialized skills and a job is waiting for them.
For most illegal immigrants, a legal option simply doesn't exist. Under current law, a young Mexican or Salvadoran who wants to improve his life by moving to America and working hard at a useful job generally has just two options: (a) Enter illegally, or (b) stay out forever. Several hundred thousand a year choose option (a).