is it late to apply for h1 from chennai ?

[cool_dude]

Hello friends

A chennai consultant company was initially ready to sponsor h1b for me.This is for entering US in this oct(05).Then he told me yesterday(may 25th) that
they need to find out whether it is late to apply for h1b or not and only then they will apply.so is it late to apply in may end or june 1st week for h1 visa.i mean is that consultancy at risk of rejection if they apply at this time.

Please let me know what you guys think ? anyone in chennai still applying for h1b after may ?