I doubt it. The number H1Bs for people with the equivalent of a Masters degree or Phd is something like one percent of all H1B visas. I seriously doubt that a

I doubt it. The number H1Bs for people with the equivalent of a Masters degree or Phd is something like one percent of all H1B visas. I seriously doubt that a shortage of H1B visas would be an issue for a company that decides to hire someone into a senior position. Senior positions are handled with more care then junior positions.