Time lag between H1 stamping and actual date at port of entry.

Hello, I am India and I have got my H1B visa stamed on Oct 29th through some company. Now I am serving my notice in my current company of 3 months which would be Jan end (i can not buy out this because of project compulsions and if i dont serve complete notice i will loose on important service related documents. )

But the company that sponsored my visa is kind of pushing to be in US by beginning of Jan and mentioned that there might be issues at port of entry if there is a gap of 3+ months between H1 stamping and actual entry in US.

Pls help me understand is that a thing to worry or is it just that my H1 sponsor is just pushing me to be in US asap for his obvious income gains. ? Thanks in advance !

It might not be a big issue, at the same time U must be able to explain the reason and convince them if asked

So, be prepared