US travel dates problem

i have my h1 stamped yesterday and in my offer letter it was given joining date as 17th oct. Due to notice period issues in my present company(India), i will be not able to travel before 17th oct and can make it in Dec only.

Conveyed the same to Employer and he said its up to u…My question are:

  1. If i travel in Dec, will i face any issues at Port of Entry like if the start date is oct 17 th, why are u coming now??(Dec)

  2. How wil be the job market in this last quarter?

It should not be an issue. You can say that you have current obligations with old employer. If possible get an updated offer letter from new employer.