My experience is telling them you need sponsorship on the phone, then 90% of
them will stop calling you again. I had three recuitiers scheduled me
interviews after i told them i need sponsorship, after interviews no one
called me again. Besides, i found my two jobs in the USA by using the
network of my univesity and monster.com, for someone like us no green card,
recuitiers is not a good choice to find your job. It is just kind of waste
time. That is just my own opinion.